Question 263757
(A solution provided by another tutor provides the correct solution by it does not use 2 equations and two variables as the problem specifies.)<br>
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.<br>
So the equations are:
x + 10 = y
and
{{{0.07*x + 0.155*10 = 0.12*y}}}
With the first equation already solved for y, using the Substitution Method seems easiest. So we'll substitute into the second equation for y:
{{{0.07*x + 0.155*10 = 0.12*(x+10)}}}
Now we have a one-variable equation to solve. First we'll simplify:
{{{0.07x + 1.55 = 0.12x + 1.2}}}
I'll get rig of the decimals by multiplying both sides by 100:
{{{7x + 155 = 12x + 120}}}
Next we'll get the variable on just one side by subtracting 7x from each side:
{{{155 = 5x + 120}}}
Subtract 120 from each side:
{{{35 = 5x}}}
Divide both sides by 5:
{{{7 = x}}}
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.