   SEARCH HOME Math Central Quandaries & Queries  Question from Ryan, a student: Two times one number plus 7 times another number is equal to 17. the first number plus the second number is equal to 25. What are the two numbers? Please Help! Hi Ryan,

This is an algebra problem so you need to decide on variable names for the two unknown numbers. I am going to call the first number j and the second k. The first sentence in your problem reads:

Two times one number plus 7 times another number is equal to 17.

Using j and k this is

Two times j plus 7 times k is equal to 17.

Using the mathematical symbols for times, plus and equal to this becomes:

2j + 7k = 17.

Using the second sentence generate a second equation involving j and k. It is then straightforward to convert this second equation into an equation of the form j = an expression involving k. Substitute this for j in the first equation and solve for k.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.