Three friends go into the bookshop. Billy buys a mystery novel and a science book. He pays £19.94. Gemma buys the same science book and an atlas. Her bill comes to £28.98. Louis buys the mystery novel and the atlas and pays £24.94. What is the price of each book?
Answers
Answer:
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Answer:
Let's use variables to represent the price of each book. We'll use:
m for the price of the mystery novel
s for the price of the science book
a for the price of the atlas
From the given information, we can set up a system of three equations:
Billy buys a mystery novel and a science book, and pays £19.94:
m + s = 19.94
Gemma buys the same science book and an atlas, and pays £28.98:
s + a = 28.98
Louis buys the mystery novel and the atlas, and pays £24.94:
m + a = 24.94
We can now solve this system of equations using substitution or elimination. Let's use elimination. First, let's subtract the second equation from the first equation:
m + s - (s + a) = 19.94 - 28.98
m - a = -9.04
Next, let's add the third equation to this result:
m - a + (m + a) = -9.04 + 24.94
2m = 15.9
Finally, let's solve for m:
m = 15.9 / 2
m = 7.95
Now that we know the price of the mystery novel, we can use any of the original equations to solve for the other prices. Let's use the first equation:
m + s = 19.94
Substituting m = 7.95, we get:
7.95 + s = 19.94
Solving for s, we get:
s = 11.99
Finally, we can use the third equation to solve for the price of the atlas:
m + a = 24.94
Substituting m = 7.95, we get:
7.95 + a = 24.94
Solving for a, we get:
a = 16.99
Therefore, the price of the mystery novel is £7.95, the price of the science book is £11.99, and the price of the atlas is £16.99.