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Math 10 Pre-IB
Solving 2 x 2 Word Problems
Please use the following three examples to help you set up and solve the word problems on the
other side of the page.
Very Important Steps
 Read the question carefully
 Define your variables (don’t always have to be x and y)
 Generate two equations and use them to solve for your two variables.
 NO guessing and checking – I need to see the algebra!
Example One:
Two numbers have a sum of 29 and differ by 15. Find the numbers.
Let one number be x and the other number be y.
 x  y  29
 x  y  15
Now use substitution or
elimination to solve for x and y!
Example Two:
Bob has $2.35 in change in his pocket consisting of just dimes and nickels. He has 31 coins in
total. How many does he have of each type?
Let d be the number of dimes.
Let n be the number of nickels. (the word “number” is important when you define variables)
 n  d  31
(the how many equation)
 .05n  .10d  2.35 (the how much equation)
Notice the money value of the nickel
and dime had to be included!
Example Three:
The corner store mixes cashews and peanuts together for a mixed bag of nuts. Cashews normally
sell for $3.20/kg and peanuts sell for $2.20/kg. The bag of mixed nuts weighs 200 kg and sells
for $2.50/kg. How many kg of cashews were sued, how many kg of peanuts were used?
Let c be the number of kg of cashews.
Let p be the number of kg of peanuts.
 c  p  200
(the how many equation)
 3.20c  2.20 p  200(2.50) (total cost needs to include the weight and the price)