Math CentralQuandaries & Queries


Question from nympha, a student:

Fifty votes were cast in class election, Beth got 1/5 of the votes. Helen got as many votes as Jane and Peter put it together. Peter got 1/3 as much votes as Jane. How much votes did each of the four candidates received?

Hi there.

Four candidates means four variables: B, H, J, P. To solve for four variables, we need to find four equations from the information given:

"Fifty votes were cast"

B + H + J + P = 50

"Beth got 1/5 of the votes"

B = (1/5) 50

"Helen got as many votes as Jane and Peter put together"

H = J + P

"Peter got 1/3 as many votes as Jane"

P = (1/3) J

So these are the four equations. Now do some substitutions into the top equation using the other equations. For example, If you substitution the third equation into the first, then the H in the first equation gets replaced by what H equals in the third equation, so you now have:

B + (J + P) + J + P = 50

If you continue this substitution, you will end up with an equation you can rapidly solve for P, so you know the value of P. B is very easy and if you use these values of P and B in the equation above, you can quickly solve for J.

Hope this helps,
Stephen La Rocque.

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