Tricky Question?

Question

Rachel has $100 in her savings account and deposits an additional $25 per week. Joanna has $350 in her account and is saving $5 per week. After how many weeks will the two girls have the same amount of money? You must use an algebraic equation to solve.

Answer 1

Use equation 100 + 25x = 350 + 5x, where x is the number of weeks. After 12 weeks Rachel will have $400 and Joanna will have $410. After 13 weeks Rachel will have $425 and Joanna will have $415. Weeks 12 and 13 are when they'll be closest to having the same amount of money. But their amounts will never be equal. x in the equation equals 12.5.

Answer 2

Rachel:
100 + 25x = y
where x is the number of weeks and y is the total saved.

Joanna:
350 + 5x = y
where x is the number of weeks and y is the total saved.

x will be the same value for both girls, because the problem says so.

y will be the same value for both girls, because the problem says so.

Subtracting the 2 equations
100 + 25x = y
350 + 5x = y
gives the following single equation:
-250 + 20 x = 0
250 = 20 x
x = 250 / 20
x = 12.5

Answer 3

Given:

y = amount in an account
x = number of weeks of deposits

The equation for Rachel's account would be:

y = 25x + 100

The equation for Joanna's account would be:

y = 5x + 350

To determine when they'll have the same amount in their accounts just set them equal:

5x + 350 = 25x + 100
250 = 20x

x = 12.5

In 12.5 weeks they'll have the same amount of money.

Answer 4

100 + 25x = 350 + 5x
Subtract 100 from both sides
25x = 250 + 5x
Subtract 5x from both sides
20x = 250
Divide by 20
x = 12.5

Answer 5

100+T*25 = 350+T*5
25T-5T = 350-100
20T = 250
T = 250 /20 = 12.5 weeks

Answer 6

1) 100+25x=350+5x
2) 100+20x=350
3) 20x=250
4) x=12.5
12 and a half weeks