Question

Amelia and Carmen read every night. Amelia reads the same number of pages each night. So does Carmen. The table shows the number of pages that each girl has left to read after 2, 4, 5, and 7 nights of reading their books.

Pages Left to Read
Nights
Amelia
Carmen
2
225
224
4
175
160
5
150
128
7
100
64

Whose book has the greater number of pages?
Amelia’s book has 1 more page.
Amelia’s book has 36 more pages.
Carmen’s book has 7 more pages.
Carmen’s book has 13 more pages.

Answer 1

Let Amelia’s starting pages be A and Carmen’s be C.

From Amelia’s table: 225 after 2 nights and 175 after 4 nights → she reads (225 − 175) / 2 = 25 pages per night.
So A = 225 + 2·25 = 275.

From Carmen’s table: 224 after 2 nights and 160 after 4 nights → she reads (224 − 160) / 2 = 32 pages per night.
So C = 224 + 2·32 = 288.

288 − 275 = 13, so Carmen’s book has 13 more pages.