Solution mixture word problem

Question

A dealer has gasoline worth 30 cents a gallon and some worth35 cents a gallon. How many gallons of each kind must he take to produce 50 gallons worth 32 cents a gallon?

Answer 1

Nathan, let's call each gallon of 30-cent gas a and each gallon of 35-cent b.

 

If we need 50 gallons total, a + b = 50

 

As far as the mixtures, 30a + 35b = 32(50)

 

Now, we "solve" the first equation for either a or b. Let's do a.

 

a = 50 - b 

 

Now we substitute this "value" for a in the 2nd equation.

 

30(50 - b) + 35b = 1600

1500 - 30b + 35b = 1600

5b = 100

b = 20

 

a = 50 - b = 50 - 20 = 30

 

Hope this helps!