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

2 Answers
Dec 16, 2016

Answer:

#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)

Dec 16, 2016

Answer:

#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.
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#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