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 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. $500, 6 weeks
B. $600, 4 weeks
C. $650, 3 weeks
D. $700, 2 weeks

800=50x+B and 950=75x+B, where B is the amount you started and X is the number of weeks you saved your money, you would get that the number of weeks you saved your money is 6 and the amount you started out with is $500

75(6)+500=950

50(6)+500=800

Hope this helped <3

Answer Link

adefunkeadewole adefunkeadewole · Answer 2 · 2021-10-08T13:43:25+02:00

This question can be solved using simultaneous equations.

Simultaneous equations are algebraic equations that both have an unknown variable called x and y. These unknown variables are related and simultaneous to each other.

The amount you started to save with is $500 and you saved for 6 weeks.

Let's represent:

The amount you and your friend started with = x

Let the number of weeks = w

Our system of equations is written as:

You save $75 per week and by vacation time, you have $950:

x + 75w = 950.........Equation 1

Your friend saves $50 per weekend by vacation time, you have $800

x + 50w = 800.......Equation 2

We subtract Equation 2 from Equation 1

25w = 150

Divide both sides by 25

25w/25 = 150/25

w = 6

Therefore, the number of weeks you both saved was 6 weeks.

Solving for the amount you started to saved with, we use Equation 1

x + 75 x 6 = 950

x + 450 = 950

Subtract 450 from both sides.

x + 450 - 450 = 950 - 450

x = 500

Therefore, the amount you started to save with was $500

Option A is the correct option.

To learn more, visit the link below:

https://brainly.com/question/14052877