Question

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Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Ea
worth either 5 points or 2 points. Write a system of equations that can be used to find how many pro
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points

Answer 1

Answer: See Below

Explanation:

Let x represent the 5-point questions

Let y represent the 2-point questions.

Points Equation: 5x + 2y = 100

Total Questions: x + y = 29

`\large\boxed{\text{System:}\bigg\{\begin{array}{c}5x+2y=100&x+y=29\\\end{array}\bigg\}}`

To solve, use Elimination Method

• multiply the bottom equation by -5
• solve for y
• input y into either equation to solve for x

`.\quad 5x+2y=100\quad \rightarrow \ \ \quad5x+2y=\ \ 100\\-5(x+y=29)\quad \ \rightarrow \quad \underline{-5x-5y=-145}\\.\qquad \qquad \qquad \qquad \qquad \qquad \ -3y=-\ 45\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad y=\quad 15\\`

x + y = 29

x = 15 = 29

x = 14

There are 14 five-point questions and 15 two-point questions on the test.