You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save $75 per week, and your f

snowlovelydayM 2021-02-06 Answered
You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save $75 per week, and your friend saves $50 per week. When the vacation time comes, you have $950, and your friend has $800. How much did you start with, and for how many weeks did you save?
A. $150, 8 weeks
B. $75, 3 weeks
C. $500, 5 weeks
D. $500, 6 weeks
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Expert Answer

Macsen Nixon
Answered 2021-02-07 Author has 117 answers
Given:
Two persons start with same amount and save for vacation for the same number of weeks.
One person saves $75 per week and has $950 at the vacation time.
Another one saves $50 per week and has $800 at the vacation time.
Let $x be the starting amount and y be the number of weeks.
From the given information,
x+75y=950----1
x+50y=800----2
Solve equations (1) and (2) and obtain the values of x and y as follows.
Subtract equation (2) from (1) and obtain the value of y as shown below.
x+75y-(x+50y)=950-800
x+75y-x-50y=950-800
25y=150
y=(150)/(25)
y= 6 weeks
now substitute y=6 in equation 1 and obtain the value of c as follows:
x+75y=950
x+75(6)=950
x+450=950
x=950-450
x=$500
Therefore , they start with $500 and save for 6 weeks
Option D is correct
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