Question

A potter makes vases and mugs. One day she sold 4 vases and 3 mugs for $80. Another day she sold 3 vases and 6 mugs for $90. How much does each vase cost? How much does each mug cost?

Answer 1

Vase: $14; Mug: $8

Explanation:

The question asks for the costs of each vase and of each mug. Since we don't know these values yet, we can use variable v to represent the cost of each vase and variable m to represent the cost of each mug.

We are told that 4 vases and 3 mugs cost $80.

So 4v + 3m = 80.

We are also told that 3 vases and 6 mugs cost $90.

So 3v + 6m = 90.

Now, there are many approaches to solve these two equations, but the most straightforward for this particular question would be to subtract one of the equations from the other.

Since 3v can be conveniently subtracted from 4v to give you v.

4v + 3m = 80

- (3v + 6m = 90)

-------------------------

v - 3m = -10

Isolate variable v.

v = 3m - 10

Now, substitute v = 3m - 10 into either one of the original equations.

4v + 3m = 80

4(3m-10) + 3m = 80

12m - 40 + 3m = 80

15m - 40 = 80

15m = 120

m = 120/15 = 8

Since m = 8, we know that each mug costs 8 dollars.

Now, substitute m = 8 into the equation again to find the cost of each vase.

4v + 3m = 80

4v + 3(8) = 80

4v + 24 = 80

4v = 56

v = 14.

Since v = 14, we know that each vase costs 14 dollars.

You can check your answer by plugging in both.

4(14) + 3(8) = 80

56 + 24 = 80

80 = 80