Question

Beth has $150 in his savings account and save $4 a month June only has $100 in her savings account but saves at the rate of $50 a month. when will June have saved more than Beth. Write an inequality to represent each relationship.

Answer 1

Answer:

2.17 months; June will have saved more than Beth after 2.17 months.

Step-by-step explanation:

Write a formula for each person showing the amount of money saved.

Beth:  $150 + ($4/mo)x, where x is the # of months.

June:  $100 + ($50/mo)x.

Equate these two formulas:

            $150 + ($4/mo)x = $100 + ($50/mo)x

Solve for x.  Combine like terms:  $100= ($46/mo)x, or x = 2.17 months.

Now, using inequalities:

$150 + ($4/mo)x < $100 + ($50/mo)x

or:  $100 < ($46/mo)x, or x > 2.17 months.  After 2.17 months, June will have saved  more than Beth (due to her saving much more per month than Beth).