Question 1206592
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The poor wording allows for different interpretations of the given information.<br>
"... he gave 50% of the rest of the salary to his parents and saved the rest of the $350..."<br>
The best interpretation of that exact wording is that he had $350 left after food and transportation, of which he gave 50% to his parents.<br>
But it could also be interpreted as saying that $350 is the amount he saved.<br>
The tutors here (most of them, anyway) are not going to spend time trying to help you with the problem if they don't know for sure what the given information is.<br>
Clean up the wording and re-post.<br>
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Added after seeing the response from tutor @ikleyn....<br>
The backwards method of solving problems like this is useful, and for many problems similar to this one it is easier to use.  It is especially useful if the steps say things like "he spent 1/5 of his salary plus $40 on food...".<br>
However, in this problem, all the steps are just using certain fractions or percentages of the remaining amounts, without any of those "... plus $40..." phrases.  That makes solving the problem "forwards" easier than solving it backwards.<br>
He spent 1/5 of his salary on food; the fraction he has left is 4/5.
He then spent 2/3 of that 4/5 of his salary on transportation, so what he has left is 1/3 of 4/5 of his salary, or 4/15 of his salary.
He then gave 50% (1/2) of what he had left to his parents, so what he had left was 1/2 of 4/15 of his salary, or 2/15 of his salary.  So he saved 2/15 of his salary.<br>
Now we come to the problem with the exact wording of the problem.<br>
If the problem said he saved "THE REMAINING $350", it would mean that he gave his parents $350 and saved the last $350.<br>
But the problem says "...he gave 50% of the REST OF THE salary to his parents and saved the REST OF THE $350". Grammatically, that means the $350 is what was left after he paid for food and transportation, and that he gave half of it to his parents and saved the other half.  So the amount he saved was $175 -- NOT $350.<br>
He spent 1/5 = 3/15 of his salary on food.
He spent 8/15 of his salary on transportation.
He gave 2/15 of his salary to his parents.
He saved 2/15 of his salary.<br>
The total he spent on food and transportation was 11/15 of his salary.  That is 11/2 of what he saved.<br>
If the amount he saved was $350 (grammatically incorrect), then the amount he spent on food and transportation was (11/2)$350 = $1925.<br>
If the amount he saved was $175 (grammatically correct), then the amount he spent on food and transportation was (11/2)$175 = $962.50.<br>