Atest has 19 questions worth a total 100 points. there are ten-point questions and four-point questions. how many questions of each kind?

10 points: 4 questions: 4*10=40
4 points: 15 questions: 4*15=60
60+40=100
hope it helps

X + y = 19

10x + 4y = 100

This is a systems of equations. 

Isolate x from the first equation:
x = 19 - y

Now, plug it into the second:

10(19 - y) + 4y = 100
190 - 10y + 4y = 100
-6y + 190 = 100
-6y = -90
y = 15

Plug y in and solve for x:
10x + 4(15) = 100
10x + 60 = 100
10x = 40
x = 4

There are four 10-point questions and fifteen 4-point questions.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

There should only be 1 solution