Mrs Bond bought 3 cans of corn and 5 cans of tomatoes for $5.46.

Question

The following week, she bought 2 cans of corn and 3 cans of tomatoes for $3.33, paying the same prices. Find the cost of a can of corn and the cost of a can of tomatoes.

Answer 1

C = price of a can of corn

T = price of a can of tomatoes

 

Let's set up our equations.

 

Week 1)      3C + 5T = 5.46

Week 2)      2C + 3T = 3.33

 

Let's multiply equation 1) by 2 and multiply equation 2) by 3.  This will give us 6C in each equation.

 

2 * Week 1)  6C + 10T = 10.92

3 * Week 2)  6C +  9T  =  9.99

 

We can now subtract equation 2) from equation 1)

T = 0.93  

So a can of tomatoes costs 93 cents.

 

To determine the price of a can of corn, we need to use the price of a can of tomatoes in either of the original equations and solve for C

2C + 3T = 3.33

2C + 3(0.93) = 3.33

2C + 2.79 = 3.33

2C = 0.54

C = 0.27

 

A can of corn costs 27 cents.

 

Hope this has helped.