Question

You have $15 in your savings account. Your friend has $25 in their savings account. You both start saving $5 per week. Write a system of linear equations that represents this situation. Will you ever have the same amount of money as your friend?

Answer 1

Answer: 15 + 5x = 25 + 5x. You will never have the same amount of savings as your friend.

Explanation:

• Set up two equations equal to one another like 15 + 5x = 25 + 5x to find out if you'll have the same savings as your friend.

• Subtract 15 on both sides to get 5x by itself. This should leave you with 5x = 10 + 5x.

• Subtract 5x on both sides to get 10 by itself. This should leave you with 0x = 10. This means that you'll never have the same amount of money because the x's cancel each other out.

Hence, 15 + 5x = 25 + 5x. You will never have the same amount of savings as your friend.

Answer 2

15 + 5x = 25 + 5x

You will never have the same amount of money as your friend.

Explanation:

Let x be the number of weeks that have passed since you and your friend started saving.

The amount of money in your savings account after x weeks is 15 + 5x.

The amount of money in your friend's savings account after x weeks is 25 + 5x.

Therefore, the system of linear equations that represents this situation is:

15 + 5x = y (equation for your savings account)

25 + 5x = z (equation for your friend's savings account)

where y represents the amount of money in your savings account after x weeks and z represents the amount of money in your friend's savings account after x weeks.

To determine if you will ever have the same amount of money as your friend, we can solve the system of equations by setting y equal to z:

15 + 5x = 25 + 5x

Simplifying, we see that the equation reduces to:

15 = 25

This is a contradiction, since 15 is not equal to 25. Therefore, there is no solution to this system of equations in which y is equal to z, which means that you will never have the same amount of money as your friend.