Pg 282 problem 7

Question

You spend $20 total on tubes of paint and disposable brushes for an art project. Tubes of paint cost $4.00 each and paintbrushes cost $0.50 each. You purchase twice as many brushes as tubes of paint. How many brushes and tubes of paint do you purchase?

Answer 1

Hello Ashlyn!

I hope that this helps!

We are going to be using two expressions to describe this question. For variables, let's call the number of paint tubes 't' and number of paint brushes 'b'.

We are first going to make an expression to describe the prices of what was purchased.

A single Paint Tubes (t) costs $4.00

A single Paint brush (b) costs $0.50 .

The total amount spent was $20.

So,

4t+0.5b=20

But we still need to describe the amounts of everything that was purchased, so we have to make another equation...

2t=b

^This equation shows that the amount of paint brushes (b) purchased was double the amount of paint tubes (t) that were purchased. This was mentioned in the prompt.

So now we are left with these expressions:

4t+0.5b=20

2t=b

Now you must use some method to solve for this system of linear equations. I will just combine. b=2t. So, I will be plugging 2t into the top equation in b's place holder. *Because b is technically equal to 2t).

(b=2t)

So now...

4t + 0.5b =20

4t + 0.5(2t) = 20

becomes

4t + t = 20

Simplify

5t=20

Divide both sides by 5.

We are now left with t =4. So the amount of paint tubes purchased was 4. We now know what t is, so we can plug t=4 into either equation to find what b is. I will be using the second equation (b=2t):

b=2t

(t=4) so...

b= 2(4)

b=8.

So b = 8 and t =4.

Let's plug these values into the first equation to double check.

4t+0.5b=20

4(4) + 0.5(8)=20

16+4= 20.

These solutions would be correct.

So,

8 Paintbrushes and 4 paint tubes were purchased :)

Answer 2

number of tubes of paint = x

number of brushes = 2x

cost of x tubes of pain = 4x

cost of 2x brushes = 2x*0.5 = x

total cost = 20

4x + x = 20

5x = 20

x = 4

4 tubes of paint

2*4 = 8 paint brushes