Question

On January 1, Trisha put $100 into a savings account that earns interest. That same day, Mark put some money into another savings account that also earns interest. After 5 years, Trisha’s account balance is 145% of her original balance, and Mark’s is 160% of his original balance. Mark and Trisha withdraw all of their money and use it to spend $225 at the amusement park. If together they have $40 left from their withdrawals after the amusement park, how much did Mark put into his savings account?

Trisha thinks that if Mark also put $100 into his account, then they would had more than $100 left after the amusement park. Is she correct or not? Explain.

Answer 1

• Mark deposited $75
• Trisha is not correct

Explanation:

The total of their account balances is equal to the total spent plus the remaining amount. The given relations tell us ...

• Trisha withdrew $100 × 145% = $145
• Mark withdrew d × 160% = 1.6d . . . for some initial deposit d
• $145 + 1.6d = $225 +40 . . . . . withdrawals = spent + change

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a.

Solving this equation, we can find Mark's withdrawal and his initial deposit.

145 +1.6d = 265

1.6d = 120 . . . . . . . the amount Mark withdrew

d = 120/1.6 = 75 . . . . the amount Mark deposited

Mark put $75 into his savings account.

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b.

Had Mark put $100 into his savings account, the total of withdrawals would have been ...

Trisha + Mark = $100 × 145% +$100 ×160% = $145 +160 = $305

After spending $225 of this amount, they would have had a leftover amount of ...

$305 -225 = $80

Trisha is not correct in her thinking that there would be more than $100 left over.