Word Problem

AsilKing

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Nov 23, 2021
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I know the answer. I need to know the steps. If 8 2/3 quarts of strawberries cost $1 39/50, what is the price of 1 quart?
 

Otis

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Apr 22, 2015
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$1.00/2 Quarts = .50
That's correct, and it's what we call a rate: $0.50 per quart.

In other words, you divided total dollars by total quarts, and the result is [imath]\frac{\text{DOLLARS}}{\text{QUART}}[/imath] or dollars per one quart.

The dollars-per-quart rate is what they're asking for in your exercise, too. Total cost is [imath]1+\frac{39}{50}[/imath] dollars and total quarts is [imath]8+\frac{2}{3}[/imath].

Convert the mixed numbers to improper fractions first, then use the rule for dividing fractions.

Also, I'm thinking that they probably want an exact answer, written as a reduced, proper fraction (i.e., not a decimal number) -- like writing 1/2 instead of 0.50.

I think I'm missing a step with the fractions.
Are you implying that you've already tried dividing the given numbers? If so, then please share your work. Otherwise, I'm not sure what you mean.

:)
 

AsilKing

New member
Joined
Nov 23, 2021
Messages
6
That's correct, and it's what we call a rate: $0.50 per quart.

In other words, you divided total dollars by total quarts, and the result is [imath]\frac{\text{DOLLARS}}{\text{QUART}}[/imath] or dollars per one quart.

The dollars-per-quart rate is what they're asking for in your exercise, too. Total cost is [imath]1+\frac{39}{50}[/imath] dollars and total quarts is [imath]8+\frac{2}{3}[/imath].

Convert the mixed numbers to improper fractions first, then use the rule for dividing fractions.

Also, I'm thinking that they probably want an exact answer, written as a reduced, proper fraction (i.e., not a decimal number) -- like writing 1/2 instead of 0.50.

I think I'm missing a step with the fractions.
Are you implying that you've already tried dividing the given numbers? If so, then please share your work. Otherwise, I'm not sure what you mean.

:)
Yes. I tried dividing the numbers. $1 39/50 divided by 8 2/3 quarts
89/50 X 26/3
89/50 X 3/26 = 267/1300
267 divided by 1300 = .2053846
The answer in the book shows 20 7/13 cents.
I'm not sure how it got 7/13.
 

Otis

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Apr 22, 2015
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89/50 [÷] 26/3
89/50 X 3/26 = 267/1300 ...
= .2053846
Correct. But, let's forget about decimal approximations.

The answer in the book shows 20 7/13 cents.
Oh, for Pete's sake. They gave you the money unit "dollars", but they want the answer written in "cents"? (They could have said so, in the instructions.)

Okay, let's convert 267/1300 dollars to cents.

:)
 

Otis

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Apr 22, 2015
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Isn't converting dollars to cents dividing 267 by 1300?
No, that division is not a unit conversion; we began by comparing dollars to quarts, so the result compares dollars to quarts.

267/1300 means 267/1300ths of a dollar for each quart, not 267/1300ths of a penny per quart.

Just like dividing $1 by 2 quarts doesn't yield 50 cents per quart. It yields 1/2 dollar per quart. We then convert 1/2 dollar to 50 cents.

If you need help converting 267/1300 dollar to cents, let us know.

:)
 

Otis

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Apr 22, 2015
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3,821
I guess I do need help converting fractions of dollars to cents.
Hi. The conversion from dollars to cents is the same whether the dollars are Whole numbers, fractions or decimal numbers (doesn't matter). Multiply by 100 cents per dollar.

Example: Convert 1/2 dollar to cents. We multiply (1/2 dollar) times (100 cents/dollar), as shown below with unit cancellations.

\(\displaystyle \frac{1}{2} \; \frac{\text{dollar}}{1} \;\; \times \;\; \frac{100}{1} \; \frac{\text{cents}}{\text{dollar}}\)


\(\displaystyle \frac{1}{\cancel{2}_{\; 1}} \; \frac{\bcancel{\text{dollar}}}{1} \;\; \times \;\; \frac{\cancel{100}^{\; 50}}{1} \; \frac{\text{cents}}{\bcancel{\text{dollar}}} \;\; = \;\; 50 \; \text{cents}\)

Once we understand the unit conversion, we simply multiply 1/2 by 100.

\(\displaystyle \frac{1}{2} \times 100 = 50\)

How many cents is 11/25 dollar? It's 44 cents.

\(\displaystyle \frac{11}{25} \times 100 = 44\)

:)
 
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