Answer:
The number of questions worth 5 points is 14 and the number of questions worth 2 points is 15. 70 points can be gained from the 5 point questions and 30 points can be gained from the 2 point questions making a total of 100 points.
Step-by-step explanation:
For this problem, we have to solve for x and y. We are given two equations.
x + y = 29
5x + 2y = 100
Let's find the value of x first. We can rearrange the first equation so it'll be easier to find the value of x using the second equation.
x + y = 29 → y = -x + 29
Now, let's plug in this equation into the second equation.
5x + 2(-x + 29) = 100
Distribute 2 to (-x + 29)
5x - 2x + 58 = 100
Combine like terms.
3x + 58 = 100
Subtract 58 from 100.
3x = 42
Divide by 3 on both sides.
x = 14
So, the value of x is 14.
Now, let's find the value of y. We can do this by plugging in our x into the first equation.
14 + y = 29
Subtract 14 from 29.
y = 15
So, the value of y is 15.
