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

Question

you have 10 more math problems than science problems. how many problems do you have in each subject? use a system of linear equations to justify your answer.

Answer 1

First define your variables.

 

Let m = # of math problems

Let s = # of science problems

 

m + s = 42   <-- Because there are 42 total problems

 

m = s + 10   <-- Because there are 10 more math problems

 

Solve by substitution method, replace m in the first equation with s + 10

 

s + 10 + s = 42   

 

2s + 10 = 42  <-- Combine like terms 

     - 10     -10

 

      2s = 32 

 

        s = 16  <-- Divide by 2

 

We now have s, so we can plug it back into an original equation to find m

 

m = s + 10  =>  m = 16 + 10 =>  m = 26

 

To confirm, we note that 16 + 26 = 42 so both equations are satisfied.

Answer 2

Let number of science problems = x

number of math problems = y

 

10 more math than science so : y = x + 10

total is 42 so:  x+y= 42

 

substitute: x + x +10= 42

2x +10 =42

 

x=16. U have 16 science problems

 

y=10+16=26. You have 26 math problems 

Answer 3

Let

M = number of math problems

S = number of science problems

 

First thing you are given is that there are a total of 42 math and science problems.  That means that:

M + S = 42

 

Second fact you are given is that there are 10 more math problems than science problems.  That means that:

 

M = S  + 10

 

 

If you substitute this value of M in the first equation (M+S=42), then:

 

S + 10 + S = 42

2S + 10 = 42

2S = 42 - 10 = 32

S = 32 / 2 = 16

 

The, since M = S + 10, M = 16 + 10 = 26

 

So the number of Science problems is 16

The number of Math problems is 26