This one is a good exercise in translating word problems into a system of equations.

According to a poll in Rockview, 1/3 of the men and 2/3 of the women are planning to vote for Bill Jones. On the election day, one and a half times more men voted than women. According to the poll, what fraction of the total vote is expected to be cast for Jones?

Solution #1:     Translate into equations.

How many will be voting for Jones:               1/3(M) + 2/3(W)   =    Jones

What is the total vote?                                        M   +     W      =        Total

What is the relationship between M and W?              M =   3/2(W)

Now we set up the fraction of the Jones vote and substitute for M:

Jones               =          (1/3)M + (2/3)W          =          (1/3)((3/2)W)   +   (2/3)W                                                                                                                            Total                                   M  +  W                                   (3/2)W  +    W

As expected, the W’s divide out:

1/2  +   2/3       =          7/6        =        7/15                                                                                                                                                                                        3/2  +  2/2                    5/2

Solution #2:     Use a round number of total voters that fits well with the fractions, such as 150.

If the number of men voting was 3/2 more than women: w + 3/2w = 150, so w = 60 and m = 90.

Now we can see that 1/3(90) = 30 men voted for Jones, and 2/3(60) = 40 women voted for Jones

Putting these together to calculate the fraction for Jones:      30 + 40            =          7                                                                                                                                                                                                                       150                           15

 

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