Math CentralQuandaries & Queries


Question from sandy, a parent:

Each boy gets 5 toys. Each girl gets 3 toys. There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls?

Hi Sandy,

Suppose the number of boys is $b$ and the number of girls is $g,$ then $b + g = 150.$

What is the total number of toys given to boys? What is the total number of toys given to girls? The number given to boys is 74 more than the number given to girls. This gives you a second equation in $b$ and $g.$ Solve the pair of equations for $b$ and $g.$


Sandy wrote back

I am not sure is is 113 boys and 27 girls.
Is that right?


Hi Sandy,

I know this can't be correct since $113 + 27 = 140 \mbox{ not } 150.$

I didn't complete the problem before I sent my first response so I decided now to complete it and see what the answer is. Each boy gets 5 toys so all together the boys get $5b$ toys. Similarly the girls get $3g$ toys. The boys got 74 more toys than the girls so

\[5b = 3g + 74.\]

I then solved the first equation, $b + g = 150$ for $g$ to get $g = 150 - b$ and substituted this into the second equation giving

\[5b = 3\left( 150 - b \right) + 74\]

which simplified to

\[8b = 450 + 74 = 524\]

or \[b = 65 \frac12.\]

What 65 and a half boys? Something is wrong with this problem. You can check my algebra but I think I am correct. It works fine if you replace "The boys had 74 more toys than girls." by "The boys had 70 more toys than girls."


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS