Question

After reading 3/4 of a magazine on Sunday, .2 of the remainder on Monday, and 10 pages on Tuesday, Michael still had to read 42 pages of the magazine. How many pages did he read on Sunday?

Answer 1

Amount Micheal read on sunday = 156 pages

Explanation:

let the total number of pages in the magazine = x

On sunday: 3/4 of the total

= 3/4 × x

Amount read on Sunday = 3x/4

On monday: 0.2 of the remainder

The remainder = total - 3x/4

= x - 3x/4

The remainder = x/4

0.2 of the remainder = 0.2 × x/4

= 2/10 × x/4 = 2x/40

Amount read on Monday = x/20

Amount read on Tuesday = 10 pages

Amount remaining for Micheal to red = 42 pages

The total pages in the magazine = Amount read on sunday + Amount read on Monday + Amount read on Tuesday + Amount remaining to be read

x = 3x/4 + x/20 + 10 + 42

collect like terms:

x - 3x/4 - x/20 = 10 + 42

$\begin{gathered} \frac{x}{1}-\frac{3x}{4}-\frac{x}{20}=10+42 \\ \frac{20(x)-5(3x)-1(x)}{20}=\text{ 52} \end{gathered}$$\begin{gathered} \frac{20x-15x-x}{20}=\text{ 52} \\ \frac{4x}{20}=\text{ 52} \\ \text{cross multiply:} \\ 4x\text{ = 52}\times20 \\ 4\text{x = 1040} \\ \frac{4x}{4\text{ }}=\text{= 1040/4} \\ x\text{ = 260} \end{gathered}$

The total number of pages in the magazine = 260 pages

Amount Micheal read on sunday = 3x/4 = 3(260)/4 = = 780/4

Amount Micheal read on sunday = 156 pages