A test is worth 100 points. There is a total of 26 questions. Spelling questions are worth 2 points each and vocab questions are worth 5 points each.

The spelling questions are 10, while the vocab questions are 16.

Step-by-step explanation: Let the spelling questions be represented by letter p, while the vocab questions should be represented by v. If there is a total of 16 questions as stated, then p + v = 26

Also if there are a total of 100 points obtainable in the test, then spelling questions times 2 points (2p) plus vocab questions times 5 points (5v) equals 100 points. This can be expressed as 2p + 5v = 100

We now have a pair of simultaneous equations as follows

p + v = 26 ———(1)

2p + 5v = 100 ———(2)

Make p the subject of the equation in equation (1). p = 26 - v. Next substitute for the value of p into equation (2)

2(26 - v) + 5v = 100

52 - 2v + 5v = 100

We collect like terms and we have

5v - 2v = 100 - 52

3v = 48

Divide both sides of the equation by 3

v = 16

Now having calculated v, substitute for the value of v into equation (1)

p + 16 = 26

Subtract 16 from both sides of the equation

p = 10

Therefore, the spelling questions equals 10 in all. While the vocab questions equals 16 in all.

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