Question

3) Both Sabrina and Rex are saving money for a big purchase. Sabrina currently

(week 0) has $112 saved, and Rex has $84 saved. Sabrina saves $10 each week
and Rex saves $15 each week. After how many weeks will Rex have more money
saved than Sabrina?

Answer 1

Approx 6 weeks

Explanation:

Represent Sabrina's savings by S(w) = $112 + ($10/wk)w, and

Rex's by R(w) = $84 + ($15/wk)w.

Equate these to determine the number of weeks it will take for their respective savings to become equal:

$112 + ($10/wk)w = $84 + ($15/wk)w

first, combine the constant dollar amounts:

$112 - $84 + ($10/wk)w = ($5/wk)w

next, subtract ($5/wk)w from both sides, obtaining:

$28 = ($5/wk)w

Finally, divide both sides by ($5/wk)w, obtaining:

w = 5.6 weeks

Thus, the answer here is that Rex will have more money saved than Sabrina after 5.6 weeks; we could round that off to 6 weeks.