Question

The Ashland High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Eaton has requested 97 earth science textbooks and 71 physics textbooks for all of her classes, which costs the department a total of $7,624. Mr. Newman has asked for 95 earth science textbooks and 93 physics textbooks, which will cost a total of $8,640. How much do the textbooks cost?

Earth science textbooks cost $______
Physics textbooks cost $______

a) $78,432; $92,160
b) $78,432; $81,720
c) $78,624; $81,720
d) $78,624; $92,160

Answer 1

By setting up a system of linear equations, we determine that each earth science textbook costs $42 and each physics textbook costs $50.

Step-by-step explanation:

To find out how much earth science and physics textbooks cost individually, we can set up two equations using the information given.

• Ms. Eaton's request: 97 earth science books (E) + 71 physics books (P) = $7,624
• Mr. Newman's request: 95 earth science books (E) + 93 physics books (P) = $8,640

We can write this as a system of linear equations:

1. 97E + 71P = 7624
2. 95E + 93P = 8640

By solving this system of equations, we can determine the individual costs of the textbooks.

To solve this, we can multiply the first equation by 95 and the second equation by 97 to align our E terms so we can eliminate them:

1. (97E + 71P) * 95 = 7624 * 95
2. (95E + 93P) * 97 = 8640 * 97

This gives us two new equations:

1. 9215E + 6745P = 724280
2. 9215E + 9021P = 837880

Now, we subtract the second equation from the first:

• 9215E + 6745P - (9215E + 9021P) = 724280 - 837880
• 0E + (-2276P) = -113600

This simplifies to:

• -2276P = -113600
• P = 113600 / 2276
• P = $50

With the price of physics textbooks (P) known, we can plug it back into one of our original equations to find the price of earth science textbooks (E).

1. 97E + 71($50) = 7624

Which simplifies to:

• 97E + 3550 = 7624
• 97E = 7624 - 3550
• 97E = 4074
• E = 4074 / 97
• E = $42

Therefore, earth science textbooks cost $42, and physics textbooks cost $50.