Question

dalia buys 20 collectible gems per month. grace sells 10 gems from her collection of 120 each month. when will dalia have more gems than grace? show your work.

Explanation:

Step1: Define variables and equations

Let $m$ = number of months.
Dalia's total gems: $20m$
Grace's total gems: $120 - 10m$
We need $20m > 120 - 10m$

Step2: Isolate the variable term

Add $10m$ to both sides:
$20m + 10m > 120 - 10m + 10m$
$30m > 120$

Step3: Solve for m

Divide both sides by 30:
$\frac{30m}{30} > \frac{120}{30}$
$m > 4$

Answer:

Dalia will have more gems than Grace after 4 months, meaning starting in the 5th month.