Question

Lyle and Shaun open savings accounts at the same time. Lyle deposits $100 initially and adds $20 per week. Shaun deposits $500 initially and adds $10 per week. Lyle wants to know when he will have the same amount in his savings account as Shaun has.

Part A: Write two equations to represent the amounts of money Lyle and Shaun have in their accounts.
a) Lyle: $100 + 20w; Shaun: $500 + 10w
b) Lyle: $500 + 10w; Shaun: $100 + 20w
c) Lyle: $100 + 10w; Shaun: $500 + 20w
d) Lyle: $500 + 20w; Shaun: $100 + 10w

Answer 1

Lyle and Shaun have two different savings accounts with different deposit patterns. The correct equations for their savings accounts are: Lyle's is $100 + 20w and Shaun's is $500 + 10w. After 40 weeks, they will have the same amount in their accounts.

Step-by-step explanation:

To find out when Lyle will have the same amount in his savings account as Shaun, we need to use algebra to solve a system of linear equations based on their respective weekly deposit patterns and their initial deposits. The correct equations that represent the amounts of money in Lyle's and Shaun's savings accounts are:

• Lyle: $100 + 20w
• Shaun: $500 + 10w

Where 'w' represents the number of weeks after they opened their accounts.

To determine the week when their savings accounts have the same amount, we need to set these two equations equal to each other and solve for 'w':

$100 + 20w = $500 + 10w

Subtracting $100 and 10w from both sides gives us:

10w = $400

Dividing both sides by 10, we find that w = 40 weeks.

So, after 40 weeks, Lyle and Shaun will have the same amount of money in their savings accounts.