How long will it be before you both have the same amount of money

Question

You have $60 and your sister has $120. You saving $7 per week and your sister is saving $5 per week. How long will it be before you and your sister have the same amount of money?

Answer 1

Let X be a number of weeks, than you have

(60 + 7 * X) - ( 120 + 5 * X) = 0

Solve for X and you get X = 30 weeks

The key here is to recognize that when they both have equal amounts the difference between their amounts will be 0.

Answer 2

For both people we have an initial amount of savings and rate at which they save. Let x be the number of weeks that pass, and y be how much you have any week. You start with $60 and save at $7 / week, your sister with $70 initially and $5 / week savings

y = 7x + 60 for you

y = 5x + 70 for your sister

Both are in the standard slope intercept form of equations. The slope is the savings per week, the y-intercept is the amount saved initial - at week zero. You will both have the same amount saved when the two lines intersect, that is, when

7x + 60 - 5x = 70

Solve for x

Answer 3