Question

Help Please!!!

（Algebra）

I know the answer but I want to know the process.

The correct answer is "6" times, but why???

Lakshmi is trying to throw basketballs through hoops at a fair. If a ball goes through a hoop, she receives 50p, but if it does not she has to pay 20p for the shot. After 15 shots, Lakshmi finds she has made a profit of £1.20. How many times did Lakshmi successfully throw a ball through a hoop?

Answer 1

Answer:

6 shots

Explanation:

Let the no. of successful shots be x,

and that of missed shots be y.

given,

x + y = 15 (total no. of shots) (eq.1)

Now,

for each successful shot, lakshmi gets 50p, so total amt. won by her = 50x

and, for each shot missed, she loses 20 p, so total amt. lost by her = 20y

given,

50x - 20y = Rs.1.20

In 1.20 Rs, no. of paise = 120,

so,

50x - 20y = 120 (eq.2)

From eq.1,

x = 15 - y

Putting the above eq. in eq.2,

50 (15 - y) - 20y = 120

750 - 50y - 20y = 120

750 - 70y = 120

750 - 120 = 70y

630 = 70y

or, y = 630/70 = 9

Now,

x = 15 - y (from 1)

so,

x = 15 - 9 = 6

Hence, the no. of successful shots made by Lakshmi = 6

I hope I have made it clear to you :)