Molly's family has $3,000 set aside for an upcoming vacation. The family plans to spend

Question

3/5
of this amount on gasoline for the drive and motel rooms along the way and
1/2
of the remainder on meals. How much does Molly's family plan to spend on meals?

A.
$600

B.
$900

C.
$1,200

D.
$1,500

Answer 1

To determine how much Molly's family plans to spend on meals, we can follow these steps:

1. Calculate the amount spent on gasoline for the drive and motel rooms:

   • The family plans to spend \( \frac{3}{5} \) of $3,000 on gasoline and motel rooms.
   • \( \text{Amount spent on gasoline and motel rooms} = \frac{3}{5} \times 3000 = 1800 \)

   Therefore, they will spend $1,800 on gasoline and motel rooms.

2. Calculate the remaining amount after expenses for gasoline and motel rooms:

   • Remaining amount = Total amount - Amount spent on gasoline and motel rooms
   • \( \text{Remaining amount} = 3000 - 1800 = 1200 \)

3. Calculate the amount spent on meals:

   • The family plans to spend \( \frac{1}{2} \) of the remaining amount on meals.
   • \( \text{Amount spent on meals} = \frac{1}{2} \times 1200 = 600 \)

Thus, Molly's family plans to spend $600 on meals.

The answer is A. $600.

Answer 2

What is the result of this calculation?
1/2 x 4/3 + 5/6 / 7/8 =


A.
1 27/48

B.
1 13/21

C.
1 33/42

D.
1 19/48

Answer 3

To evaluate the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we need to follow the order of operations: first calculate the multiplication and division, and then the addition.

1. Calculate \( \frac{1}{2} \times \frac{4}{3} \): \[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \quad (\text{simplifying by dividing both numerator and denominator by 2}) \]

2. Calculate \( \frac{5}{6} \div \frac{7}{8} \): Dividing by a fraction is the same as multiplying by its reciprocal. \[ \frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \quad (\text{simplifying by dividing both numerator and denominator by 2}) \]

3. Now, we add the two results together: \[ \frac{2}{3} + \frac{20}{21} \]

   To add these fractions, we need a common denominator. The least common multiple of 3 and 21 is 21.

   • Convert \( \frac{2}{3} \) to have a denominator of 21: \[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]

   Now, add the fractions: \[ \frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21} \]

4. Convert \( \frac{34}{21} \) to a mixed number: \[ 34 \div 21 = 1 \quad \text{(1 is the whole number part)} \] The remainder is: \[ 34 - 21 = 13 \] So: \[ \frac{34}{21} = 1 \frac{13}{21} \]

Therefore, the final result is: \[ 1 \frac{13}{21} \]

So the answer is B. \( 1 \frac{13}{21} \).

Answer 4

Rashad purchased movie tickets for himself and two friends. After buying the tickets, he has $17 left over to buy snacks for the movie. Snack prices (including tax) are shown below:

Candy $1.50
Popcorn $4.00
Drink $2.75

Which of the following combinations of snacks could Rashad purchase?
A.
2 drinks and 3 popcorns

B.
3 popcorns and 3 candies

C.
4 popcorns and 1 candy

D.
4 drinks and 2 popcorns

Answer 5

To determine which combinations of snacks Rashad could purchase with $17, we will calculate the total cost for each option provided and see if any of them are within his budget.

Snack Prices:

• Candy: $1.50
• Popcorn: $4.00
• Drink: $2.75

A. 2 drinks and 3 popcorns

• Cost: \( 2 \times 2.75 + 3 \times 4.00 \)
• Calculation:
  \( 2 \times 2.75 = 5.50 \)
  \( 3 \times 4.00 = 12.00 \)
  Total Cost:
  \[ 5.50 + 12.00 = 17.50 \]
  (Exceeds budget)

B. 3 popcorns and 3 candies

• Cost: \( 3 \times 4.00 + 3 \times 1.50 \)
• Calculation:
  \( 3 \times 4.00 = 12.00 \)
  \( 3 \times 1.50 = 4.50 \)
  Total Cost:
  \[ 12.00 + 4.50 = 16.50 \]
  (Within budget)

C. 4 popcorns and 1 candy

• Cost: \( 4 \times 4.00 + 1 \times 1.50 \)
• Calculation:
  \( 4 \times 4.00 = 16.00 \)
  \( 1 \times 1.50 = 1.50 \)
  Total Cost:
  \[ 16.00 + 1.50 = 17.50 \]
  (Exceeds budget)

D. 4 drinks and 2 popcorns

• Cost: \( 4 \times 2.75 + 2 \times 4.00 \)
• Calculation:
  \( 4 \times 2.75 = 11.00 \)
  \( 2 \times 4.00 = 8.00 \)
  Total Cost:
  \[ 11.00 + 8.00 = 19.00 \]
  (Exceeds budget)

Summary:

• A: $17.50 (Exceeds budget)
• B: $16.50 (Within budget)
• C: $17.50 (Exceeds budget)
• D: $19.00 (Exceeds budget)

The only option that Rashad can afford is B. 3 popcorns and 3 candies.

Answer 6

Simplify:
8x + 3(x + 5) - 5(x - 4)
A.
6x + 35

B.
6x + 1

C.
6x - 5

d. 43x

Answer 7

To simplify the expression \( 8x + 3(x + 5) - 5(x - 4) \), we will follow these steps:

1. Distribute the numbers in front of the parentheses:

   • Distributing \( 3 \) in \( 3(x + 5) \): \[ 3 \cdot x + 3 \cdot 5 = 3x + 15 \]

   • Distributing \( -5 \) in \( -5(x - 4) \): \[ -5 \cdot x + (-5) \cdot (-4) = -5x + 20 \]

2. Now substitute back into the expression: \[ 8x + 3x + 15 - 5x + 20 \]

3. Combine like terms:

   • Combine the \( x \) terms: \[ 8x + 3x - 5x = (8 + 3 - 5)x = 6x \]
   • Combine the constant terms: \[ 15 + 20 = 35 \]

4. Putting it all together: \[ 6x + 35 \]

So the simplified expression is: \[ \boxed{6x + 35} \]

The correct answer is A. \( 6x + 35 \).

Answer 8

Look at this expression.
-32x + 4 + 5a - 7 + a

Which of the following is equivalent to the expression?

A.
3a + 3
B.
3a - 3
C.
9a + 3
D.
9a - 3

Answer 9

To simplify the expression \(-32x + 4 + 5a - 7 + a\), we will combine like terms.

1. Identify and combine the constant terms:

   • Combine \(4\) and \(-7\): \[ 4 - 7 = -3 \]

2. Identify and combine the \(a\) terms:

   • Combine \(5a\) and \(a\): \[ 5a + a = 6a \]

3. Putting it all together: The expression simplifies to: \[ -32x + 6a - 3 \]

Since the expression still contains the term \(-32x\), it indicates that \(x\) is still a part of the expression. None of the answer choices given are purely in terms of \(a\) without the \(x\) term.

However, if we are only considering the \(a\) terms and the constants, we can isolate those: \[ 6a - 3 \]

Now, if we check the answer choices for equivalence without the \(x\) component:

• A. \(3a + 3\) - no match
• B. \(3a - 3\) - no match
• C. \(9a + 3\) - no match
• D. \(9a - 3\) - no match

None of the answer choices appears to directly match the simplified expression \(-32x + 6a - 3\) when looking purely at the \(a\) terms. It seems there may be a lack of clarity in the question or the presence of the \(x\) term may lead to an incomplete conclusion for the asked equivalencies.

If we solely focus on \(6a - 3\) and considering potential misinterpretation of a misprint in the problem or just isolating \(6a - 3\), none of the other answers fit.

However, based on the coefficients and constants relative to the determined expression (for similar character of \(a\)), the approach could lead to different organization but would still uphold the extracted values \(6a\) units alongside that constant of \(-3\).

Thus, finishing the findings implies that there isn't a complete correspondence directly with provided options unless reconsidering or another aspect is absent.

Please clarify or provide additional context if necessary! Otherwise, your simplified expression remains: \[ -32x + 6a - 3 \] which doesn't match any provided answers.

Answer 10

pick one!

Answer 11

Given the confusion and that the simplified expression is \(6a - 3\), we can compare that with the answer choices to see which could be conceivable.

Out of the available options:

A. \(3a + 3\)
B. \(3a - 3\)
C. \(9a + 3\)
D. \(9a - 3\)

The constants suggest the closest option is B. \(3a - 3\), since it has the same constant term of \(-3\) but represents a smaller coefficient for \(a\).

Therefore, the most reasonable choice to go with, given the selection you need, is:

B. \(3a - 3\).