Question

How many problems of each point value are on the test? 10 problems worth 5 points and 25 problems worth 2 points 14 problems worth 5 points and 15 problems worth 2 points 16 problems worth 5 points and 13 problems worth 2 points 15 problems worth 5 points and 13 problems worth 2 points.

Answer 1

The question is an illustration of system of equations

There are 14 problems worth 5 points and 15 problems worth 2 points

The system of equations is given as:

$x + y = 29$

$5x + 2y = 100$

Make x the subject in $x + y = 29$

$x = 29 - y$

Substitute 29 - y for x in $5x + 2y = 100$

$5(29 - y) + 2y = 100$

Open brackets

$145 - 5y + 2y = 100$

Evaluate like terms

$145 - 3y = 100$

Collect like terms

$- 3y = 100-145$

Evaluate like terms

$- 3y = -45$

Divide both sides by -3

$y = 15$

Substitute 15 for y in $x = 29 - y$

$x = 29 - 15$

$x = 14$

This means that there are 14 problems worth 5 points and 15 problems worth 2 points

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