SOLUTION: Mrs Lee bought 40 fun fair coupons. Some of the coupons were worth $2 and the rest were worth $5. The total value of all the coupons was $146. How many $5 coupons did Mrs Lee buy?

Question 123892: Mrs Lee bought 40 fun fair coupons. Some of the coupons were worth $2 and the rest were worth $5. The total value of all the coupons was $146. How many $5 coupons did Mrs Lee buy?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let T represent the number of $2 coupons and F represent the number of $5 coupons.
.
The problem tells you that a total of 40 coupons were purchased. Therefore, we can write an equation
about the total number of coupons. The numbers of each type of coupon must total 40. In equation
form this is:
.
T + F = 40
.
The number of dollars spent on $2 coupons is the $2 multiplied by the number of $2 coupons purchased.
Since the number of $2 coupons purchased is the unknown T, the total dollar value of the $2
coupons is $2 times T or simply 2T. Similarly, the amount spent of $5 coupons is $5 times the
number of $5 coupons purchased or $5 times F or simply 5F. The total spent is $146, so we can
write the equation totaling the amounts spent for each type of coupon as:
.
2T + 5F = 146
.
Returning to the first equation for the total number of coupons sold we can subtract
F from both sides of the equation to find that:
.
T = 40 - F
.
So we can substitute 40 - F for its equivalent value T. Making this substitution into the dollar
equation we get:
.
2(40 - F) + 5F = 146
.
Doing the distributed multiplication on the left side results in:
.
80 - 2F + 5F = 146
.
The two terms containing F (the terms are -2F and + 5F) combine to give 3F, which reduces the
equation to:
.
80 + 3F = 146
.
Get rid of the 80 on the left side by subtracting 80 from both sides. This further reduces
the equation to:
.
3F = 66
.
Solve for F by dividing both sides of this equation by 3 to get:
.
F = 22
.
This tells you that 22 five dollar coupons were purchased.
.
Since a total of 40 coupons were bought, this means that the number of $2 coupons was
40 - 22 or 18.
.
Let's check the money spent. If 22 coupons were purchased at $5 each, a total of $110 was spent
(from $5 times 22).
.
And if 18 coupons were purchased at $2 each, a total of $36 was spent for these coupons.
.
This means that the total amount spent on coupons was $110 + $36 and that does total to $146
just as it should.
.
Hope this helps you to understand the problem.
.
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