# 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 You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## 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
$y=\left(150\right)/\left(25\right)$
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