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

Answer:

Carmen’s book has 13 more pages.

Step-by-step explanation:

After night 4, Amelia has 175 pages remaining.  After night 5, she has 150.  This means she reads 175-150 = 25 pages per night.

After night 4, Carmen has 160 pages remaining.  After night 5, she has 128.  This means she reads 160-128 = 32 pages per night.

Let x be the total number of pages in Amelia's book.  She reads 25 pages per night; after 4 nights, she has 175 pages remaining.  This gives us the equation

x - 25(4) = 175

x - 100 = 175

Add 100 to each side:

x - 100 + 100 = 175+100

x = 275

Amelia's book has 275 pages.

Let y be the total number of pages in Carmen's book.  She reads 32 pages per night; after 4 nights, she has 160 pages remaining.  This gives us the equation

x - 32(4) = 160

x - 128 = 160

Add 128 to each side:

x - 128 + 128 = 160 + 128

x = 288

Carmen's book has 288 pages.

This means Carmen's book has 288-275 = 13 more pages.

Answer 2

Answer:

Carmen's book by 13 pages.

Step-by-step explanation:

Step one

225-175 to get 50 pages per every 2 night for Amelia

Step two

224- 160 to get 64 pages every 2 night for Carmen

Step 3

Add 225 and 50 to get 275

Step 4

Add 224 and 64 o get 288

Step 5

Subtract 275 from 288 to get 13