Question

Joshua has math and reading homework tonight. Joshua can solve each math problem in 2.5 minutes and he can read each page in 3 minutes. The number of pages Joshua read is twice the number of math problems he solved. and it took him 59.5 minutes to complete all of his homework. Determine the number of math problems Joshua solved and the number of pages he read

Answer 1

Answer:

Joshua solved 7 math problems and tread 14 pages.

Step-by-step explanation:

Let x be the number of math problems Joshua solved. The number of pages Joshua read is twice the number of math problems he solved, then 2x is the number of pages Joshua read.

Joshua can solve each math problem in 2.5 minutes, then x math problems he solves in 2.5x minutes.

Joshua can read each page in 3 minutes, then 2x pages he reads in $3\cdot 2x=6x$ minutes.

It took him 59.5 minutes to complete all of his homework, so

$2.5x+6x=59.5$

Solve this equation:

$2.5x+6x=59.5\\ \\8.5x=59.5\\ \\85x=595\\ \\x=7\\ \\2x=14$

Joshua solved 7 math problems and tread 14 pages.

Answer 2

For this case we propose a system of equations:

x: Let the variable representing the number of math problems result

y: Let the variable representing the number of pages read

According to the statement data we have:

$2.5x + 3y = 59.5\\y = 2x$

Substituting the second equation into the first we have:

$2.5x + 3 (2x) = 59.5\\2.5x + 6x = 59.5\\8.5x = 59.5\\x = \frac {59.5} {8.5}\\x = 7$

So, Joshua solved 7 math problems.

On the other hand we have:

$y = 2 (7) = 14$

So, Joshua read 14 pages.

Answer:

Joshua solved 7 math problems and read 14 pages.