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3 years ago

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a language arts test is worth 100 points there is a total of 26 questions . there are spelling word questions that ae worth 2 po

ints each and vocabulary word question worth 5 points each. how many of each type of question are there

1 answer:

natka813 [3]3 years ago

4 0

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

<em><u>Solution:</u></em>

Let "x" be the number of spelling word questions

Let "y" be the number of vocabulary word question

<em><u>There is a total of 26 questions. Therefore, we get</u></em>

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

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

<em><u>There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each</u></em>

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

<em><u>Let us solve eqn 1 and eqn 2</u></em>

From eqn 1,

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

<em><u>Substitute eqn 3 in eqn 2</u></em>

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

3y = 100 - 52

3y = 48

<h3>y = 16</h3>

<em><u>Substitute y = 16 in eqn 3</u></em>

x = 26 - 16

<h3>x = 10</h3>

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

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