# Can you solve this simple math problem?

Here is a problem of a type that I would think occurs fairly often.

The Senate votes on a proposal. The ratio of votes in favor to votes against the proposal is 7 to 4. If 99 senators voted, how many votes were there for and against the proposal?

Can you solve this without using algebra?

Observing members:
0
Composing members:
0
## 3 Answers

sure. 7+4=11

99/11=9

7*9=63

4*9=36

SImple

It is simple, but I wonder if most people would be able to solve it. Does it help that this is a problem involving whole numbers? What if the problem had been this: Someone walked 5.7 miles and the ratio for walking in the morning to walking in the afernoon is 4 to 3. How far did the person walk in the morning and in the afternoon?

I was looking at a high school level book, and it took an algebraic approach, which is really kind of ugly: If x is the number of people who voted in favor then 99 – x voted against, so we have x/(99-x) = 7/4. Truly awful.

IBefore teaching algebra, it might be a good idea to teach different types of problems that can be solved without algebra. It teaches mathematical manipulation and provides some interest to see how these same problems can be solved with algebra.

Here is another one. Since I have not had many visitors, I will also give the solution. You can try to find the solution before reading it.

The sum of two numbers is 20 and the difference between the two numbers is 6. What are the two numbers?

Solution:

Let’s start by looking at both numbers equal to 10. The sum is 20, but the difference is 0. If we add 1 to one of the tens and subtract 1 from the other, we still have the sum being 20, but now the difference is 2, since adding and subtracting 1 will each increase the difference by 1. It therefore follows that by adding a number to one 10 and subtracting the number from the other 10 will give a sum of 20 and a difference of twice the number. To get a difference of 6 we add and subtract 3, giving 10+3=13 and 10–3=7.

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