SOLUTION: Translate the problem into a pair of linear equations in two variables.Solve the equations using either elimination or substitution. Problem: A contractor mixes concrete from b

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Question 263757: Translate the problem into a pair of linear equations in two variables.Solve the equations using either elimination or substitution.
Problem:
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 7% cement should he mix with 10 bags of 15.5% cement to produce a mix containing 12% cement?
Found 2 solutions by mananth, jsmallt9:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Translate the problem into a pair of linear equations in two variables.Solve the equations using either elimination or substitution.
Problem:
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 7% cement should he mix with 10 bags of 15.5% cement to produce a mix containing 12% cement?
let the total no of bags be x
then x-10 will be number of bags with 7% cement
x-10*0.07+0.155*10= x*0.12
0.07x- 0.7+1.55=0.12x
-0.05x =-0.85
x= 17 bags
7 bags of 7% cement will have to be mixed

Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
(A solution provided by another tutor provides the correct solution by it does not use 2 equations and two variables as the problem specifies.)

We have two unknowns in this problem: The number of bags of 7% cement and the total number of bags used. So
Let x = the number of bags of 7% cement, and
y = the total number of bags of 12% cement.

So the equations are:
x + 10 = y
and

With the first equation already solved for y, using the Substitution Method seems easiest. So we'll substitute into the second equation for y:

Now we have a one-variable equation to solve. First we'll simplify:

I'll get rig of the decimals by multiplying both sides by 100:

Next we'll get the variable on just one side by subtracting 7x from each side:

Subtract 120 from each side:

Divide both sides by 5:

Since the question is how many bags of 7% cement are used and since x is this number, we don't really care about y. The answer to the question is 7.