Answer: 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.
