SOLUTION: Lauren is shooting at a target at afair. If she hits the target she recieves 50 pences,but if she misses she has to pay 20 pences for the shot. After 15 shots, Lauren finds she has

Question 204227This question is from textbook Longman Mathematics for IGCSE
: Lauren is shooting at a target at afair. If she hits the target she recieves 50 pences,but if she misses she has to pay 20 pences for the shot. After 15 shots, Lauren finds she has made a profit of 1.20 pounds. How many hits has she had? This question is from textbook Longman Mathematics for IGCSE

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Lauren is shooting at a target at afair. If she hits the target she recieves 50 pences,but if she misses she has to pay 20 pences for the shot. After 15 shots, Lauren finds she has made a profit of 1.20 pounds. How many hits has she had?
.
Let h = number of hits
and m = number of misses
.
Since we have two unknowns, we'll need two equations.
Equation 1 is derived from the fact she took 15 shots:
h + m = 15
.
Equation 2 is derived from the profit of 1.20
(100 pences is equivalent to 1 pound)
(50/100)h - (20/100)m = 1.20
50h - 20m = 120
5h - 2m = 12
.
Using the "substitution method", we solve equation 1 for m:
h + m = 15
m = 15-h
.
We substitute the above into equation 2 and solve for h:
5h - 2m = 12
5h - 2(15-h) = 12
5h - (30-2h) = 12
5h - 30 + 2h = 12
7h - 30 = 12
7h = 42
h = 6
.
Solution: 6 hits

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