Question 1 (1 point)

Question

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A landscaping company ordered 17 plants and 8 trees for a total of $964. If plants are $12 each, write and solve a linear equation to determine the cost of each tree.

Question 1 options:

$204

$95

$12

$952

Question 2 (1 point)

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The admission fee at a small fair is $1.50 for children and $4.00 for adults. Tuesday night, $5050 is collected. If 1,000 adults attended the fair, write and solve a linear equation to determine the number of children that attended.

Question 2 options:

400 children

1000 children

1.5 children

700 children

Question 3 (1 point)

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Determine the x-intercept and the y-intercept for the equation
x-y=1
Question 3 options:

x - intercept: (-1, 0)

y-intercept: (0, 1)

x - intercept: (1, 0)

y-intercept: (0, -1)

x - intercept: (0, 1)

y-intercept: (-1, 0)

x - intercept: (0, -1)

y-intercept: (1, 0)

Question 4 (1 point)
-2x-5y=10
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Determine the x-intercept and y-intercept for the equation

Question 4 options:

x - intercept: (0, -5)

y-intercept: (-2, 0)

x - intercept: (0, -2)

y-intercept: (-5, 0)

x - intercept: (-5, 0)

y-intercept: (0, -2)

x - intercept: (-2, 0)

y-intercept: (0, -5)

Answer 1

Let's solve each question step by step.

Question 1: A landscaping company ordered 17 plants and 8 trees for a total of $964. If plants are $12 each, write and solve a linear equation to determine the cost of each tree.

1. Let \( x \) be the cost of each tree.
2. The total cost of the plants is \( 17 \times 12 = 204 \).
3. The total cost of the trees is \( 8x \).
4. According to the problem, the total cost is given by: \[ 204 + 8x = 964 \]
5. Solving for \( x \): \[ 8x = 964 - 204 \] \[ 8x = 760 \] \[ x = \frac{760}{8} = 95 \]

Question 1 answer: $95

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Question 2: The admission fee at a fair is $1.50 for children and $4.00 for adults. If $5050 is collected and 1000 adults attended, write and solve a linear equation to determine the number of children that attended.

1. Let \( y \) be the number of children.
2. The total income from adults is \( 1000 \times 4 = 4000 \).
3. The income from children can be expressed as \( 1.50y \).
4. The total income equation is: \[ 4000 + 1.50y = 5050 \]
5. Solving for \( y \): \[ 1.50y = 5050 - 4000 \] \[ 1.50y = 1050 \] \[ y = \frac{1050}{1.50} = 700 \]

Question 2 answer: 700 children

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Question 3: Determine the x-intercept and y-intercept for the equation \( x - y = 1 \).

1. To find the x-intercept, set \( y = 0 \): \[ x - 0 = 1 \implies x = 1 \quad \text{(x-intercept is (1,0))} \]
2. To find the y-intercept, set \( x = 0 \): \[ 0 - y = 1 \implies y = -1 \quad \text{(y-intercept is (0,-1))} \]

Question 3 answer: x - intercept: (1, 0) and y - intercept: (0, -1)

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Question 4: Determine the x-intercept and y-intercept for the equation \(-2x - 5y = 10\).

1. To find the x-intercept, set \( y = 0 \): \[ -2x - 5(0) = 10 \implies -2x = 10 \implies x = -5 \quad \text{(x-intercept is (-5, 0))} \]
2. To find the y-intercept, set \( x = 0 \): \[ -2(0) - 5y = 10 \implies -5y = 10 \implies y = -2 \quad \text{(y-intercept is (0, -2))} \]

Question 4 answer: x - intercept: (-5, 0) and y - intercept: (0, -2)

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In summary:

• Question 1 answer: $95
• Question 2 answer: 700 children
• Question 3 answer: x - intercept: (1, 0), y - intercept: (0, -1)
• Question 4 answer: x - intercept: (-5, 0), y - intercept: (0, -2)