Question

Write an equation and solve: Your math homework has 6 more than three
times the number of problems you have on your history worksheet. If you
have 42 problems to do for math and history, how many math problems do
you have to complete for homework?

Answer 1

Answer: 33 math problems.

Step-by-step explanation:

Let x = Number of math problems

y= Number of history problems

According to the question , we have

$3y+6=x\ \ \ \ \ (i)\\\\ x+y=42\ \ \ \ (ii)$

We can rewrite (i) as $x-3y=6$    (iii)

Now, subtract (iii) from (ii), we get

$y-(-3y)=42-6\\\\\Rightarrow\ y+3y=36\\\\\Rightarrow\ 4y=36\\\\\Rightarrow\ y= \dfrac{36}{4}\\\\\Rightarrow\ y=9$

Put this in (i), we get

$x=3(9)+6 = 27+6=33$

Hence, you have to complete 33 math problems.