Question

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. Write and solve a system. How many problems do you have in each subject?

Answer 1

The System of equation are
`\left \{ {{m+s=42} \atop {m-s=10} \right.`

I have 26 math problems and 16 science problems.

Explanation:

Let the number of math problem be 'm'.

Let the number of Science problem be 's'.

Now Given:

You have a total of 42 math and science problems for homework.

It means Number of math problem plus number of Science problem is equal to 42.

Framing the equation we get;

`m+s=42 \ \ \ \ equation \ 1`

Also Given:

You have 10 more math problems than science problems.

It means that Number of math problem is equal to 10 plus number of Science problem.

Framing the equation we get;

`m=10+s\\\\m-s=10 \ \ \ \ equation \ 2`

Hence the System of equation are
`\left \{ {{m+s=42} \atop {m-s=10} \right.`

Now Solving the system of equation we get;

Adding equation 1 and equation 2 we get;

`(m+s)+(m-s)= 42+10\\\\m+s+m-s=52\\\\2m=52\\\\m=(52)/(2)=26`

Now Substituting the value of 'm' in equation 1 we get;

`m+s=42\\\\26+s=42\\\\s=42-26\\\\s=16`

Hence I have 26 math problems and 16 science problems.