Question

solving by substitution
mr. martin’s math test, which is worth 100 points, has 29 problems. each problem is worth either 5 points or 2 points.
let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
x + y = 29, 5x + 2y = 100
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

Explanation:

Step1: Solve the first equation for y

From \( x + y = 29 \), we can express \( y \) as \( y = 29 - x \).

Step2: Substitute y into the second equation

Substitute \( y = 29 - x \) into \( 5x + 2y = 100 \). We get \( 5x + 2(29 - x) = 100 \).

Step3: Simplify and solve for x

Expand the equation: \( 5x + 58 - 2x = 100 \). Combine like terms: \( 3x + 58 = 100 \). Subtract 58 from both sides: \( 3x = 42 \). Divide by 3: \( x = 14 \).

Step4: Find y

Substitute \( x = 14 \) into \( y = 29 - x \), so \( y = 29 - 14 = 15 \).

Answer:

B. 14 problems worth 5 points and 15 problems worth 2 points