Here is a quick and simple math hack – if the solution is left in either ratio form or expressed as a set of variables, quickly solve the ratio problem by plugging in numbers!
Example
Alice’s take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month?
- 1⁄2
- 1⁄3
- 1⁄4
- 1⁄5
- 1⁄6
Solution
- The question is asking what fraction of Alice’s take home pay did she save each month
- Identify the variables in the word problem. There are two variables in the question prompt, take home pay and amount saved:
- From the statement above, we can translate that 12y=3(x-y)
- We need to solve for y/x. Since the question is essentially asking for a ratio, we can plug in numbers as a shortcut to solve the problem! Pick an easy number to plug in. For example, x=100
Let x = total take home pay each month
y = amount saved each month
note: we are trying to solve for y/x, which is a ratio!
12y = 3(x – y)
12y = 3(100 – y)
15y = 300
15y = 300/15
y = 20
y/x = 20/100 = 1/5
The answer is D, 1/5
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