two friends, sam and alex, are saving money. sam starts with $20 and saves $5 per week. alex starts with $40…

two friends, sam and alex, are saving money. sam starts with $20 and saves $5 per week. alex starts with $40 and saves $3 per week. after how many weeks will they have the same amount of money?\na. 6\nb. 27\nc.10\nd. 4

two friends, sam and alex, are saving money. sam starts with $20 and saves $5 per week. alex starts with $40 and saves $3 per week. after how many weeks will they have the same amount of money?\na. 6\nb. 27\nc.10\nd. 4

Answer

Explanation:

Step1: Set up equations

Let $x$ be the number of weeks. Sam's money $y_1 = 20 + 5x$. Alex's money $y_2=40 + 3x$.

Step2: Set the two - equations equal

$20 + 5x=40 + 3x$.

Step3: Solve for $x$

Subtract $3x$ from both sides: $20 + 5x-3x=40 + 3x-3x$, which gives $20 + 2x=40$. Then subtract 20 from both sides: $2x=40 - 20$, so $2x = 20$. Divide both sides by 2: $x=\frac{20}{2}=10$.

Answer:

C. 10