Julie, Bruno, and Carl participated in a jump rope event as a fundraiser. Julie's mom pledged to donate $1.25 for each jump Julie completed over 100. Bruno's dad pledged to donate $6 plus $0.40 for each jump Bruno completed. Carl's grandfather pledged to donate $0.30 for each jump Carl completed. Julie's mom donated $58.75, Bruno's dad donated $58.80, and Carl's grandfather donated $54.00. Order the students from least to greatest based on the number of jumps they completed during the fundraiser.

Question

06-11-2017
Mathematics

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Julie, Bruno, and Carl participated in a jump rope event as a fundraiser. Julie's mom pledged to donate $1.25 for each jump Julie completed over 100. Bruno's dad pledged to donate $6 plus $0.40 for each jump Bruno completed. Carl's grandfather pledged to donate $0.30 for each jump Carl completed. Julie's mom donated $58.75, Bruno's dad donated $58.80, and Carl's grandfather donated $54.00. Order the students from least to greatest based on the number of jumps they completed during the fundraiser.

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meerkat18 meerkat18 · Answer 1 · 2017-11-19T10:25:20+01:00

To summarize what has been given in the problem, first list the donations given by Julie's mom (JM), Bruno's dad (BD), and Carl's grandfather (CG).

JM = $58.75
BD = $58.80
CG = $54.00

Next, we translate the word problem into equations:

(1) 58.75 = 1.25x
(2) 58.80 = 6 + 0.4y
(3) 54 = 0.30z

where,
x = number of jumps Julie completed over 100
y = number of jumps Bruno completed
z = number of jumps Carl completed

Equation (1) refers to the statement "Julie's mom pledged to donate $1.25 for each jump Julie completed over 100." Equation (2) refers to "Bruno's dad pledged to donate $6 plus $0.40 for each jump Bruno completed. " Equation (3) refers to Carl's grandfather pledged to donate $0.30 for each jump Carl completed.

Solving each equation separately, we then get:

x = 58.75/1.25 = 47
y = (58.80-6)/0.4 = 132
z = 54/0.30 = 180

Note that Julie has completed 100 jumps + 47 jumps which her Mom pledged to donate for.

Thus, the order of the students from least to greatest number of jumps is:

Bruno = 132 jumps
Julie = 147 jumps
Carl = 180 jumps