Question

a language arts test is worth 100 points there is a total of 26 questions . there are spelling word questions that ae worth 2 points each and vocabulary word question worth 5 points each. how many of each type of question are there

Answer 1

10 question of spelling words and 16 questions of vocabulary are present

Solution:

Let "x" be the number of spelling word questions

Let "y" be the number of vocabulary word question

There is a total of 26 questions. Therefore, we get

number of spelling word questions + number of vocabulary word question = 26

x + y = 26 --------- eqn 1

There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each

The language arts test is worth 100 points

Therefore, we frame a equation as:

number of spelling word questions x 2 + number of vocabulary word question x 5 = 100

$x \times 2 + y \times 5 = 100$

2x + 5y = 100 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 26 - y ------- eqn 3

Substitute eqn 3 in eqn 2

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

3y = 100 - 52

3y = 48

y = 16

Substitute y = 16 in eqn 3

x = 26 - 16

x = 10

Thus 10 question of spelling words and 16 questions of vocabulary are present