15) macy starts with $20 in her bank account and she saves $5 each week. robby has $100 in his bank account…

15) macy starts with $20 in her bank account and she saves $5 each week. robby has $100 in his bank account, and he saves $2.50 each week. after how many weeks will macy and robby have the same amount in their accounts and how much money will that be? write a system of equations to solve.\na) 25 weeks; $160\nb) 32 weeks; $180\nc) 20 weeks; $120\nd) 22 weeks; $135

15) macy starts with $20 in her bank account and she saves $5 each week. robby has $100 in his bank account, and he saves $2.50 each week. after how many weeks will macy and robby have the same amount in their accounts and how much money will that be? write a system of equations to solve.\na) 25 weeks; $160\nb) 32 weeks; $180\nc) 20 weeks; $120\nd) 22 weeks; $135

Answer

Explanation:

Step1: Define variables and equations

Let $w$ = number of weeks, $A$ = account balance. Macy's balance: $A = 20 + 5w$ Robby's balance: $A = 100 + 2.50w$

Step2: Set equations equal

$20 + 5w = 100 + 2.50w$

Step3: Solve for $w$

$5w - 2.50w = 100 - 20$ $2.50w = 80$ $w = \frac{80}{2.50} = 32$

Step4: Find account balance

Substitute $w=32$ into Macy's equation: $A = 20 + 5(32) = 20 + 160 = 180$

Answer:

B) 32 weeks; $180