paint cost $19-per-gallon is to be mixed with 5 gallons of a $3-per-gallon thinner

Question

paint cost $19-per-gallon is to be mixed with 5 gallons of a $3-per-gallon thinner to make a paint that can be solde for $14-per-gallon. how much of the cheaper paint will be produced?

Answer 1

Dalton,

You just need to set up some equations to represent the situation.

 

If X is the quantity of $19 paint and Y is the quantity of $14 paint, then we can write these two equations:

 

3gal * 5$/gal  +  Xgal * 19$/gal  =  Ygal * 14$/gal         and   Ygal  =  5gal + Xgal

 

I have included the units in the first line just to make sure you can see the relationships.

Substituting 5 + X in for Y we get:

 

3.5 + 19X = 14(5 + X)

 

3.5 + 19X = 70 + 14X

 

          5X = 66.5

 

           X = 13.3 gal of $19 paint

 

           Y = 5 + 13.3 = 18.3 gal of $14 paint

Answer 2

x=# gallons of the $19 per gallon paint

(19)(x)+(3)(5)=14(x+5)

19x+15=14x+70

19x-14x=70-15

5x=55

x=55/5

x=11 gallons of the $19 paint

11 gallons+5 gallons=16 gallons of the cheaper paint