Question

Use the three steps to solve the problem. Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?

Answer 1

118

Explanation:

Let

a = gallons of $6 syrup

b = gallons of $ 80 syrup

then

equation 1

a + b = 50

equation 2

6a + .8b /50=2.36

6a + .8b = 2.36 * 50

6a + .8b = 118

multiply equation 3 with 10

60a + 8b = 1180

multiplay equation 1 with 8 and then subt 1 from 2

(2) 60 + 8b =1180

(1) - 8a-8b=-400

52a = 780

a=15

and

a+b =50

15 + b=50

b=35

15= gallons of $6 syrup

35=gallons of $.80

6a+.8b/50 = 2.36

6(15) + .8(35)/50 =2.36

90 + 28 /50 = 2.36

118/50 = 2.36

118 = 118

Answer 2

15 gallons of maple syrup

35 gallons of corn syrup

Explanation:

Firstly, I would like to make all our currency be in cents.

Let the number of maple syrup needed be m and the number of corn syrup be c.

Now, the mixture costs 236 cents per mixture. We interpret this using the cost of each syrup to make a mathematical expression as follows:

600m + 80c = 236( m + c) ........(i)

Now we need 50 gallons, meaning, the number of both syrups add up to 50.

m + c = 50 ..........(ii)

We now solve both equations simultaneously.

From (i), we can get 364m - 156c = 0

From (ii) we get c = 50 - m

If we insert this into that expression from (i) , we get

364m - 156(50 - m ) = 0

This yields, 520m = 7800

And m = 15

Since c = 50 - m,

Then c = 50 - 15 = 35