Question

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

Answer:

number of math problems = 26

number of science problem = 16

Step-by-step explanation:

a total of 42 math and science problems for homework

Let m be the number of math problems and 's' be the number of science problems

$m+s=42$

You have 10 more math problems than science problems

$m=s+10$

substitute s+10 for m in the first equation

$m+s=42$

$s+10+s=42$

$2s+10=42$

subtract 10 from both sides

$2s = 32$

divide both sides by 2

$s= 16$

$m=s+10$

$m=16+10$

$m=26$

number of math problems = 26

number of science problem = 16

Answer 2

Answer:there are 26 math problems.

There are 16 science problems

Step-by-step explanation:

Let x represent the number of math problems that you have.

Let y represent the number of science problems that you have.

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

x + y = 42 - - - - - - - - - - 1

You have 10 more math problems than science problems. This means that

x = y + 10

Substituting x = y + 10 into equation 1, it becomes

y + 10 + y = 42

2y + 10 = 42

2y = 42 - 10 = 32

y = 32/2 = 16

Substituting y = 16 into x = y + 10, it becomes

x = 16 + 10 = 26