Question

Jesse and Margot both start reading the same book at the same time. The number of pages Margot reads each day is directly proportional to the number of pages Jesse reads each day. On Monday, Jesse read 42 pages and Margot read 60. On Tuesday, Jesse read 70 pages. How many pages did Margot read on Tuesday?

A. 28
B. 42
C. 60
D. 100
E. 112​

Answer 1

Since the number of pages Margot reads each day is directly proportional to the number of pages Jesse reads each day, we can set up a ratio based on the information given.

On Monday:
Jesse's pages: Margot's pages = 42:60

Simplifying the ratio by dividing both sides by 6:
Jesse's pages: Margot's pages = 7:10

Now, on Tuesday, if Jesse reads 70 pages:
Margot's pages = (10/7) * 70

Calculating this gives:
Margot's pages = 100

Therefore, the answer is:
D. 100

Answer 2

D

Explanation:

let Jesse be represented by j and Margot by m

given m is directly proportional to j , then the equation relating them is

m = jk ← k is the constant of proportionality

to find k, use the condition j = 42 and m = 60 ( pages read on Monday )

60 = 42k ( divide both sides by 42 )

`(60)/(42)` = k , that is

k =
`(10)/(7)`

m =
`(10)/(7)` j ← equation of proportion

when j = 70 , then

m =
`(10)/(7)` × 70 = 10 × 10 = 100

that is Margot read 100 pages on Tuesday.