Answer:
The two siblings will have saved the same amount towards their mother's gift after 3 weeks.
Amount saved by Wyatt = [tex]\$41[/tex]
Amount saved by Wyatt's sister = [tex]\$41[/tex]
Step-by-step explanation:
Let [tex]t[/tex] (in weeks) denotes the time period by which the two siblings will have saved the same amount towards their mother's gift.
Wyatt already has $20 saved and plans to save $7 per week from his allowance.
Amount saved by Wyatt = [tex]20+7t[/tex]
Wyatt's sister has $14 saved so far and will save $9 per week from hers.
Amount saved by Wyatt's sister = [tex]14+9t[/tex]
To find the time period by which the two siblings will have saved the same amount towards their mother's gift,
solve the following equation.
[tex]20+7t=14+9t\\20-14=9t-7t\\6=2t\\3=t[/tex]
So, the two siblings will have saved the same amount towards their mother's gift after 3 weeks.
Amount saved by Wyatt = [tex]20+7(3)=20+21=\$41[/tex]
Amount saved by Wyatt's sister = [tex]14+9(3)=14+27=\$41[/tex]
