Question

Jack is selling holiday ornaments and boxes of candy. Each ornament is $1.50 and each box of candy is $3.00. Jack sold a total of 15 items for $27. How many boxes of candy did he sell?

Answer 1

We can write a system of equations.

1.50x + 3.00y = 27
x + y = 15

Where x = ornaments, and y = boxes of candy.

Answer 2

So can you solve that system of equations? @Kaylaaaaaaaaaa

Answer 3

how do i do that

Answer 4

how do i do that @iGreen

Answer 5

Well we can use substitution.

x + y = 15

Solve for x:

Subtract y to both sides:

x = -y + 15

Now we can plug in -y + 15 for x in the 1st equation:

1.50x + 3.00y = 27

1.50(-y + 15) + 3.00y = 27

Distribute 1.50 into the parenthesis:

-1.50y + 22.5 + 3.00y = 27

Simplify:

1.5y + 22.5 = 27

Now subtract 22.5 to both sides, what's 27 - 22.5?

Answer 6

Can you subtract that? @Kaylaaaaaaaaaa

Answer 7

it is 4.5 @iGreen

Answer 8

Yep, that gives us:

\(1.5y = 4.5\)

Now divide 1.5 to both sides, what's 4.5 / 1.5?

Answer 9

3 @iGreen

Answer 10

Yep, so we get:

\(x = 3\)

We said ornaments were 'x', so Jack sold 3 ornaments.

It says Jack sold a total of 15 items.

So to find out how many boxes of candy he sold, subtract 15 - 3, what do you get?

Answer 11

12 @iGreen

Answer 12

Yep, so Jack sold 3 ornaments, and 12 boxes of candies.

Answer 13

thankyou @iGreen