# Question #bab68

Jan 18, 2018

$26$ math problems and $16$ science problems.

#### Explanation:

Let :

• $x =$ math problems
• $y =$ science problems

So

$x + y = 42$
$x = y + 10$

Then substitute $y + 10$ in for $x$ to solve for $y$:

$y + 10 + y = 42$

$2 y + 10 = 42$

$2 y = 32$

$y = 16$

Plug $y$ into either equation to solve for $x$:

$x = 16 + 10$

$x = 26$

Jan 18, 2018

There are $26$ math problems and $16$ science problems.

#### Explanation:

Let $x$ equal the number of science problems, and $x + 10$ equal the number of math problems. Set their sum equal to $42$. Solve for $x$.

$x + x + 10 = 42$

Simplify.

$2 x + 10 = 42$

Subtract $10$ from both sides.

$2 x + 10 - 10 = 42 - 10$

Simplify.

$2 x = 32$

Divide both sides by $2$.

$x = \frac{32}{2}$

Simplify.

$x = 16$

Number of science questions: $x = 16$

Number of math questions: $x + 10 = 16 + 10 = 26$