In June, Katherine bought 21 cans of food and 3 bags of litter for a total of $42. In July she spent $60 on 32 cans of food and 4 bags of litter. What is the cost of one bag of litter?

$1

$3

$7

$21

Question

In June, Katherine bought 21 cans of food and 3 bags of litter for a total of $42. In July she spent $60 on 32 cans of food and 4 bags of litter. What is the cost of one bag of litter?

 $1

 $3

 $7

 $21

pfenn1 · Answer

Let x = cost of a bag of cat litter and y=cost of a can of food. The first sentence implies
$$3x+21y=42$$The second sentence implies$$4x+32y=60$$ Solve the first equation for y in terms of x and plug that expression into the second equation for y.  Then rearrange and solve for x.