The expression below gives the cost, in dollars, of sending a letter to Spain: Here, is the letter's weight in ounces.
The coefficient of is the cost for each additional ounce of weight.
To illustrate:
If (we have a -ounce letter), the cost is
If (we have a -ounce letter), the cost is
If (we have a -ounce letter), the cost is
Note the following:
The number in this expression represents a unit rate. Each time we increase the letter's weight by ounce, the cost increases by .
There is also a base fee of , which does not depend on the weight of the letter. We can think of this as the cost of sending a zero-ounce letter.
The taxi fare, in dollars, charged by a particular cab company is given by the expression where is the number of miles traveled. What do the constant term and the coefficient of represent in this context?
The expression tells us that the cab company charges for each mile traveled, plus a "base fee" of
The constant term is We can think of this as the fee (in dollars) for traveling zero miles.
The coefficient of is This represents the fee (in dollars) charged for every mile traveled.
The taxi fare, in dollars, charged by a particular cab company is given by the expression $5m+10$, where $m$ is the number of miles traveled.
What does the coefficient of $m$ represent in this context?
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a
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The fee for traveling zero miles is $\$5.$ |
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b
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The driver charges a $\$5$ tip. |
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c
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The total fee for traveling $m$ miles is $5m$ dollars. |
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d
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The cab company charges $\$5$ for traveling $10$ miles. |
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e
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The taxi company charges $\$5$ for each mile traveled. |
The taxi fare, in dollars, charged by a cab company is given by the expression $6m+8$, where $m$ is the number of miles traveled.
What does the constant term of the expression represent in this context?
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a
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The fee for traveling zero miles is $\$8.$ |
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b
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The total fee for traveling $m$ miles is $6m$ dollars. |
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c
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The cab company charges $\$6$ for traveling $8$ miles. |
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d
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The fee for traveling zero miles is $\$6.$ |
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e
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The driver charges a $\$6$ tip. |
A recording studio charges musicians an initial fee of to record an album. The studio also charges an additional fee of per hour. What expression gives the cost of recording an album in terms of the number of hours
If is the number of hours used to record an album, and the studio charges an fee of per hour, then the cost for hours must be
However, there is also a fixed fee for recording an album. This fee is Consequently, the constant term of the expression should be
Therefore, the expression that represents the total cost of recording an album is:
A dance academy charges a fixed price of $\$20$ to use its facilities and $\$30$ per hour of instruction.
What expression gives the total cost, in dollars, of using the facilities for $h$ hours?
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a
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$50$ |
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b
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$30 h+20h$ |
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c
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$20 h+30$ |
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d
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$50h$ |
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e
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$30 h+20$ |
A pizzeria charges $\$15$ for a cheese pizza and $\$3$ for each topping.
What expression gives the total cost, in dollars, of a pizza with $n$ toppings?
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a
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$15n+3$ |
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b
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$15$ |
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c
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$3n+15$ |
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d
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$3n$ |
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e
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$15n+3n$ |
In many countries, a sales tax is charged whenever an individual or company makes a purchase. The tax is usually based on a certain percentage of the sale price.
For example, suppose a person purchases a bicycle for and there is a sales tax of How much is this tax, and what is the total cost of the bicycle?
To determine the amount of the tax the person must pay, we multiply , as follows:
Therefore, the purchaser must pay a sales tax. This means that the total amount the person needs to pay for the bicycle is
At a grocery store, the price of a turkey is dollars. However, there is also a sales tax.
What expression represents the total cost of a turkey after tax is applied?
The price before taxes of the turkey is dollars.
The amount of tax is of the price of the turkey, or
Therefore, the expression that represents the total cost of the turkey after tax is:
Alice is buying a handbag. The price of a handbag is $P$ dollars, and Alice also has to pay a $20\%$ tax.
What expression represents the total cost, in dollars, of a handbag after tax is applied?
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a
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$P+2P$ |
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b
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$P+20$ |
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c
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$P+20P$ |
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d
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$P+0.2$ |
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e
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$P+0.2P$ |
Abbie is buying a car. The price of the car is $C$ dollars, and he also has to pay a $15\%$ tax.
What expression represents the total cost, in dollars, of the car after tax is applied?
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a
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$C + 0.15$ |
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b
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$C + 15$ |
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c
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$C + 15C$ |
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d
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$C + 0.15C$ |
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e
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$0.15C$ |
In a particular fast-food restaurant, a standard lunch consists of hot dogs for dollars each, potato wedges for dollars each, and drink dollars. Monica went to the fast-food restaurant to pick up lunch for her family, and the total bill was dollars. What does the factor mean in this context?
Two hot dogs cost dollars, eight potato wedges cost dollars, and a drink costs dollars. Thus, each standard lunch costs dollars. Monica's bill comes to dollars, which is times the cost of a single standard lunch. Thus, the factor must be the total number of standard lunches that Monica purchased.
A bouquet of flowers consists of $3$ roses, $4$ tulips and $5$ violets. The cost of one rose is $R$ dollars, the cost of one tulip is $T$ dollars and the cost of one violet is $V$ dollars. Max is purchasing some bouquets for a wedding, and his total bill comes to $8(3R + 4T+5V)$ dollars.
What does the factor $8$ mean in this context?
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a
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Max purchased $8$ bouquets in total |
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b
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Each bouquet costs $\$8$ |
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c
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There are $8$ roses in total |
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d
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Each bouquet costs $(3R+4T+5V)$ dollars |
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e
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There are $8$ tulips in total |
A pack of markers consists of $3$ black markers for $B$ dollars each, $2$ red markers for $R$ dollars each, and one green marker for $G$ dollars. Maya purchases some packs of markers, and her total bill comes to $4(3B + 2R + G)$ dollars.
What does the factor $4$ mean in this context?
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a
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Maya purchased $4$ packs in total |
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b
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There are $4$ black markers in total |
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c
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There are $4$ markers in total |
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d
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Each pack costs $(3B + 2R + G)$ dollars |
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e
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Each pack costs $\$4$ |