Here's an example exercise.
Denis bought 62 pencils. Some are premium pencils, and some are budget pencils.
Premium pencils cost $1.80 each, and budget pencils cost $0.05 each. Altogether,
Denis paid $24.10 for his purchase.
How many premium pencils did Denis buy? How many budget pencils did Denis buy?
We're asked for two unknown numbers, so we assign symbols to represent them.
Let A = number of premium pencils
Let B = number of budget pencils
Now we can use symbols A and B, to write expressions and equations.
The
expression A + B represents the total number of
all pencils Denis bought. We know what that total is, from
the given information. We write the first
equation:
A + B = 62
That equation does not say anything about money. It only counts the pencils.
Next, we write an equation about the money. Each premium pencil costs $1.80, and Denis bought A of them, so
the money paid for premium pencils is expressed as
1.80A. (If you have trouble understanding why the expression 1.80A represents money spent on premium pencils, let us know.) Likewise,
0.05B is the expression which represents
the money paid for budget pencils. If we add these
two amounts of money together, we get the total purchase amount. We know the total purchase amount, from
the given information. We write the second
equation:
1.80A + 0.05B = 24.10
Now, there are a number of ways to find the values of A and B. I'm not sure how you solved problem #5, so I will show the substitution method.
Solve the first equation for one of the variables, and then substitute the result for the same variable in the other equation. Doing that provides a new equation containing only one variable.
I choose to solve the first equation for
B, and then I substitute the result for
B in the second equation.
A + B = 62
Subtract A from each side
B =
62 - A
Substitute this result for B in the second equation
1.80A + 0.05(
62 - A) = 24.10
See? This equation contains only one variable, so we can solve for it.
On the left-hand side, use the distributive property to multiply 0.05(62 - A)
1.80A + 0.05(62) + 0.05(-A) = 24.10
1.80A + 3.10 - 0.05A = 24.10
Combine the two like-terms
1.75A + 3.10 = 24.10
Isolate the A-term on the left, by subtracting 3.10 from each side
1.75A + 3.10 - 3.10 = 24.10 - 3.10
1.75A = 21
Divide each side by 1.75 to solve for A
1.75A / 1.75 = 21 / 1.75
A = 12
How do we find B? We use the formula for B that we already found (above).
B = 62 - A
B = 62 - 12
B = 50
So far, we think A = 12 and B = 50. Let's check those candidates (always a good idea), using our
two equations.
A + B = 62
12 + 50 = 62
1.80A + 0.05B = 24.10
1.80(12) + 0.05(50) = 24.10
21.60 + 2.50 = 24.10
I hope this example helps you to write two equations and to find the solution, for problem #6. Cheers