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2 years ago

14

There are 18 questions on the test. Each question is worth either four or five points. The total is 80 points. How many question

s of each type are on the test?

1 answer:

amm18122 years ago

8 0

Answer: the number of four point questions in the test is 10.

the number of five point questions in the test 8

Step-by-step explanation:

Let x represent the number of four point questions in the test.

Let y represent the number of five point questions in the test.

There are 18 questions on the test. It means that

x + y = 18

Each question is worth either four or five points. The total is 80 points. This means that

4x + 5y = 80 - - - - - - - - - - - - - -1

Substituting x = 18 - y into equation 1, it becomes

4(18 - y) + 5y = 80

72 - 4y + 5y = 80

- 4y + 5y = 80 - 72

y = 8

x = 18 - y = 18 - 8

x = 10

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Given:

The equation of a line is:

$2y+3x=10$

The line is dilated by factor 3.

To find:

The result of dilation.

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For $x=0$ ,

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$y=\dfrac{10}{2}$

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For $x=2$ ,

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$2y+6=10$

$2y=10-6$

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Divide both sides by 2.

$y=\dfrac{4}{2}$

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The given line passes through the two points A(0,5) and B(2,2).

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Using this rule, we get

$A(0,5)\to A'(3(0),3(5))$

$A(0,5)\to A'(0,15)$

Similarly,

$B(2,2)\to B'(3(2),3(2))$

$B(2,2)\to B'(6,6)$

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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$y-15=\dfrac{-3}{2}x$

Multiply both sides by 2.

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$2y+3x=30$

Therefore, the equation of the line after the dilation is $2y+3x=30$ .

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