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| Math Central | Quandaries & Queries |
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Question from Sindy, a student: Brandon went shopping & spent 1/4 of his money on shoes & 1/5 of the remainder on a new wallet. He then spent $\$60$ on a pair of jeans. If he had $\$60$ left, how much did Brandon start with? |
Hi Sindy,
Both problems you sent us I would call "working backwards" problems. For this problem I see 4 steps.
| Step | Action | Value before |
|---|---|---|
| 1 | Buy shoes | |
| 2 | Buy wallet | |
| 3 | Buy jeans | |
| 4 | Count what's left | $\$60$ |
At step 4 he counted his money and he had $\$60.$ At step 3 he bought a pair of jeans for $\$60$ and what he had left was $\$60$ so at step 3 he had $\$120.$
| Step | Action | Value before |
|---|---|---|
| 1 | Buy shoes | |
| 2 | Buy wallet | |
| 3 | Buy jeans | $\$120$ |
| 4 | Count what's left | $\$60$ |
At step 2 he bought a wallet with 1/5 of the money he had at this point. He was left with $\$120$ so 4/5 of the money he had at this point was $\$120.$ Since $\large \frac{120}{4} \normalsize = 30$ he spent $\$30$ on the wallet. Thus, before he bought the wallet he had $\$120 + \$30 = \$150.$
| Step | Action | Value before |
|---|---|---|
| 1 | Buy shoes | |
| 2 | Buy wallet | $\$150$ |
| 3 | Buy jeans | $\$120$ |
| 4 | Count what's left | $\$60$ |
How much did he have before he bought the shoes? Check your answer by working forward.
Now try the second problem you sent us.
Penny
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