1. Malik’s solution to the equation , when , is shown below.

Question

2/5x-4y=10
2/5x-4(60)=10
2/5x-240+240=10+240
5/2[2/5x]=5/2[250
x=265


What error did Malik make first when solving the equation ?

Malik did not multiply 5/2[250] correctly.
Malik added 240 to each side of the equation.
Malik did not multiply 5/2[2/5x] correctly.
Malik substituted 60 for y instead of x.

Answer 1

Malik made the first error by substituting 60 for y instead of substituting the correct value for x.

The original equation is \( \frac{2}{5}x - 4y = 10 \), and Malik should have replaced y with 60, but it seems from the context he confused variables or made a mistake in his substitutions. The first critical error that leads to the incorrect outcome is the faulty substitution of values into the equation.

So, the best answer is:

Malik substituted 60 for y instead of x.

Answer 2

2. What is the value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8?

20
32
44
48

3. The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?

x = 8, y = 45
x = 10, y = 22
x = 16, y = 22
x = 18, y = 18

4. What is the value of x in the equation 4 x plus 8 y equals 40, when y equals 0.8?

4.6
8.4
10
12

5. What is the value of x in the equation 8x – 2y = 48, when y = 4?

6
7
14
48

6. Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100.

1.25x + 1.49 = 100
What error did Barbara make in writing the equation?

Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara's equation did not use the correct total for sales.

7. What is the value of x in the equation 2x + 3y = 36, when y = 6?

8
9
27
36

8. What is the value of y in the equation 5x + 2y = 20, when x = 0.3?

2.5
2.8
9.25
10.75

9. What is the value of x in the equation one-fifthx – two-thirdsy = 30, when y = 15?

4
8
80
200

10. Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)

$1.75
$2.06
$2.39
$3.99

Answer 3

Let's go through each question one by one.

2. Find \( m \) in the equation \( \frac{1}{2} m - \frac{3}{4} n = 16 \) when \( n = 8 \).

Substituting \( n = 8 \):

\[ \frac{1}{2} m - \frac{3}{4} (8) = 16 \]

Calculating \( \frac{3}{4} \times 8 = 6 \):

\[ \frac{1}{2} m - 6 = 16 \]

Adding 6 to both sides:

\[ \frac{1}{2} m = 22 \]

Multiplying both sides by 2:

\[ m = 44 \]

Value of \( m \): 44

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3. Librarian's DVD Budget

The cost equation is: \[ 20x + 8y = 500 \]

Now we examine each option:

1. \( x = 8, y = 45 \): \[ 20(8) + 8(45) = 160 + 360 = 520 \quad (\text{over budget}) \]

2. \( x = 10, y = 22 \): \[ 20(10) + 8(22) = 200 + 176 = 376 \quad (\text{under budget}) \]

3. \( x = 16, y = 22 \): \[ 20(16) + 8(22) = 320 + 176 = 496 \quad (\text{under budget}) \]

4. \( x = 18, y = 18 \): \[ 20(18) + 8(18) = 360 + 144 = 504 \quad (\text{over budget}) \]

Possible choices: \( x = 10, y = 22 \) or \( x = 16, y = 22 \) (Budget allowed)

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4. Find \( x \) in the equation \( 4x + 8y = 40 \) when \( y = 0.8 \).

Substituting \( y = 0.8 \):

\[ 4x + 8(0.8) = 40 \]

Calculating \( 8 \times 0.8 = 6.4 \):

\[ 4x + 6.4 = 40 \]

Subtracting 6.4 from both sides:

\[ 4x = 33.6 \]

Dividing both sides by 4:

\[ x = 8.4 \]

Value of \( x \): 8.4

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5. Find \( x \) in the equation \( 8x - 2y = 48 \) when \( y = 4 \).

Substituting \( y = 4 \):

\[ 8x - 2(4) = 48 \]

Calculating \( 2 \times 4 = 8 \):

\[ 8x - 8 = 48 \]

Adding 8 to both sides:

\[ 8x = 56 \]

Dividing both sides by 8:

\[ x = 7 \]

Value of \( x \): 7

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6. Error in Barbara's equation

The equation is meant to consider the number of bottles sold:

\[ 1.25x + 1.49y = 100 \]

Since she only included the iced tea price but not the number of bottles of water \( y \), the correct interpretation requires that both prices multiply their respective quantities.

Error: Barbara’s equation did not consider the number of bottles of water.

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7. Find \( x \) in the equation \( 2x + 3y = 36 \) when \( y = 6 \).

Substituting \( y = 6 \):

\[ 2x + 3(6) = 36 \]

Calculating \( 3 \times 6 = 18 \):

\[ 2x + 18 = 36 \]

Subtracting 18 from both sides:

\[ 2x = 18 \]

Dividing both sides by 2:

\[ x = 9 \]

Value of \( x \): 9

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8. Find \( y \) in the equation \( 5x + 2y = 20 \) when \( x = 0.3 \).

Substituting \( x = 0.3 \):

\[ 5(0.3) + 2y = 20 \]

Calculating \( 5 \times 0.3 = 1.5 \):

\[ 1.5 + 2y = 20 \]

Subtracting 1.5 from both sides:

\[ 2y = 18.5 \]

Dividing both sides by 2:

\[ y = 9.25 \]

Value of \( y \): 9.25

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9. Find \( x \) in the equation \( \frac{1}{5}x - \frac{2}{3}sy = 30 \) when \( y = 15 \).

Note: Let's assume \( s \) just represents a constant scalar for this example; without \( s \) known it's not possible to solve for \( x \) directly.

Substituting \( y = 15 \):

\[ \frac{1}{5}x - \frac{2}{3}s(15) = 30 \]

Which leads to \( \frac{2}{3} \times 15 = 10 \):

Rearranging it becomes \( \frac{1}{5}x - 10s = 30 \) - to solve correctly would need value for \( s \).

The question's answer options suggest we don’t know; we could assume no correct answer is available without assuming \( s \).

10. Chen's Veggies and Fruits

Using cost equation:

\[ 5v + 7(2.85) = 28.70 \]

Calculating \( 7 \times 2.85 = 19.95 \):

\[ 5v + 19.95 = 28.70 \]

Subtracting 19.95 from both sides:

\[ 5v = 28.70 - 19.95 = 8.75 \]

Dividing by 5:

\[ v = 1.75 \]

Approximate price of a pint of veggies: $1.75

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In summary:

1. 44
2. \( x = 10, y = 22 \) or \( x = 16, y = 22 \)
3. 8.4
4. 7
5. Barbara's error: Number of water bottles.
6. 9
7. 9.25
8. (Requires value of \( s \))
9. $1.75