Question

justine and barbara each want to run for president of their school’s student council. in order to do so, they must collect a certain number of signatures and get a nomination. so far, justine has 16 signatures, and barbara has 15. justine is collecting signatures at an average rate of 4 per day, whereas barbara is averaging 5 signatures every day. assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. how long will that take? how many signatures will they both have? in (square) days, justine and barbara will each have collected (square) signatures.

Explanation:

Step1: Define variables & equations

Let $d$ = number of days, $J$ = total signatures for Justine, $B$ = total signatures for Barbara.
$J = 16 + 4d$
$B = 15 + 5d$

Step2: Set equations equal (same signatures)

$16 + 4d = 15 + 5d$

Step3: Solve for $d$

$16 - 15 = 5d - 4d$
$d = 1$

Step4: Calculate total signatures

Substitute $d=1$ into $J$:
$J = 16 + 4(1) = 20$

Answer:

In 1 day, Justine and Barbara will each have collected 20 signatures.