Question

How many pounds of chocolate worth $1.5 a pound must be mixed with 10 pounds of chocolate worth 60 cents a pound to produce a mixture worth $1 a pound?

Answer 1

8 pounds

Explanation:

Let x represent the amount of chocolate that is worth $1.50 per pound. This makes the total amount of this chocolate

1.5x.

The other type of chocolate is worth 60 cents, or 0.60, per pound; for 10 pounds of it, we have the expression

0.6(10).

Together, this gives us 1.5x+0.6(10).

This is to equal a chocolate that is worth $1.00 per pound. There will be 10+x pounds of this, giving us the expression

1(10+x).

This gives us the equation

1.5x+0.6(10)=1(10+x)

Simplifying the left hand side, we have

1.5x+6 = 1(10+x)

Using the distributive property on the right hand side, we have

1.5x+6 = 10+x

Subtract x from each side:

1.5x+6-x = 10+x-x

0.5x+6 = 10

Subtract 6 from each side:

0.5x+6-6 = 10-6

0.5x = 4

Divide both sides by 0.5:

0.5x/0.5 = 4/0.5

x = 8

Answer 2

`8\ pounds`

Explanation:

Let

x-----> amount of pounds of chocolate worth $1.5

we know that

`1.5x+0.60(10)=1(x+10)`

`1.5x+6=x+10`

`1.5x-x=10-6`

`0.5x=4`

`x=8\ pounds`