A test is worth 100 points. Each problem is worth either 2 points or 5 points. The number of 5-point problems is 22 fewer than the number of 2-point problems. How many problems of each type are on the test?
50 points and u will get brainlist
50 points and u will get brainlist
Answers & Comments
Step One: Since the total number of points is 38, we can create the Let Statements:
Let x= one type of question
Let 38-x= the other type of questions
Step Two: Create an equation to relate the number of questions to the price
100=5x+2(38-x) Distribute
100=5x+76-2x Subtract 76 from both sides of the equation
100-76=5x-2x Combine like terms
24=3x Divide both sides by 3
8=x
∴There are eight questions of one type and 30 questions of the other type.
Best,
Star
it is correct
There are 30 2-point problems and 8 5-point problems.
Given:
Total points in the test = 100
The number of 5-point problems is 22 less than the number of 2-point problems
To find:
The number of problems of each type.
Solution:
Let us assume that the number of 2-point problems is x.
According to the given data, the number of 5-point problems is 22 less than x.
=> The number of 5-point problems = x - 22
The total number of points adds up to 100.
=> 2x + 5 (x-22) = 100
=> 2x + 5x - 110 = 100
=> 7x = 100 + 110
=> x = 210/7
=> x = 30
=> x - 22 = 30 - 22 = 8
Hence, there are 30 2-point problems and 8 5-point problems.
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