Jesse bought 5.2 pounds of grapes for $7.75. Using the unit rate, how much would 3 pounds of grapes cost?

2 Answers
Alan P.
Dec 16, 2016

3 pounds would cost color(green)($4.47)

Explanation:

{:($7.75),("for"),(5.2" pounds"):}rArr{:(($7.75)/(5.2)~~$1.4938),("for"),(1" pound"):}

So the unit price is $1.4938 per pound.

($1.4938)/cancel("pound")xx3cancel(" pounds") = $4.47 (to the nearest cent)

Tony B
Dec 16, 2016

3lb" of grapes"=$4.47 to 2 decimal places

Explanation:

color(blue)("Determine unit cost")

In the context of this question unit rate is the cost of 1 (unit) pound of grapes.

color(brown)("Using ratio")

("cost")/("weight") ->($7.75)/(5.2)" but we need "("cost")/1

To turn the 5.2 into 1 divide it by 5.2. For multiply or divide, what we do to the bottom we also do to the top to maintain correct proportions.

("cost")/("weight") ->($7.75)/(5.2) -=($7.75-:5.2)/(5.2-:5.2) = (1.4903...)/1

To reduce rounding error use (7.75-:5.2)/1 = 7.75/5.2 as unit cost.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Determine cost of 3 pounds of grapes")

1 pound cost $7.75/5.2

1lb =$7.75/5.2

Multiply both sides by 3

3xx1lb=3xx$7.75/5.2

3lb=$4.47115....

3lb=$4.47 to 2 decimal places

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