Question

Annabelle has math and reading homework tonight. Annabelle can solve each math problem in 3 minutes and she can read each page in 2 minutes. The number of pages Annabelle read is 4 times the number of math problems she solved. and it took her 55 minutes to complete all of her homework. Determine the number of math problems Annabelle solved and the number of pages she read.

Answer 1

The number of math problems Annabelle solved = 5 problems

The number of pages Annabelle read= 20 pages

Explanation:

Given:

Time taken for Annabelle to solve one problem =3 minutes

Time taken for Annabelle to read one page =2 minutes

Total time taken by Annabelle to complete her homework= 55 minutes

To find:

Total Number of problems solved by Annabelle=?

Total Number of pages read by Annabelle=?

Solution:

Let the number of problem solved be x

Let the number of pages read be y

It is given that the number pages read is 4 times the number of problem solved

So number of pages read y= 4x

Now time taken to solve x problems = time taken to solve one problem X total number of problem

=>
`3* x`

=>
`3x`

Similarly,

Time taken to read 4x pages= total number of pages read X time taken to read one problem

=>
`(4x)* 2`

=>
`2(4x)`

Now we know that

Time taken to solve x problems + Time taken to read 4x pages= 55 minutes

3x + (4x)2=55

3x+8x=55

11x=55
`x=(55)/(11)`

x=5

So number of problem solved is x=5

Number of pages read y=4(x)=4(5)=20