Aaron works 3 1/2

Question

hours every Saturday at a rate of $7.25 per hour. He is paid every four weeks. If his boss gives him a $1.00 raise, how much will Aaron be paid in his next paycheck?
A.

$95.70

B.

$101.50

C.

$108.90

D.

$115.50

Answer 1

To calculate Aaron's next paycheck, we first need to find out how much he is currently earning and then how much he will earn after the raise.

1. Calculate his total hours worked over four weeks:
   Aaron works 3.5 hours every Saturday. Over four Saturdays (four weeks), he will work: \[ 3.5 \text{ hours/week} \times 4 \text{ weeks} = 14 \text{ hours} \]

2. Calculate his current pay for four weeks:
   His current hourly rate is $7.25, so his pay over four weeks is: \[ 14 \text{ hours} \times 7.25 \text{ dollars/hour} = 101.50 \text{ dollars} \]

3. Calculate his new hourly rate after the raise:
   His boss gives him a $1.00 raise, so his new hourly rate will be: \[ 7.25 + 1.00 = 8.25 \text{ dollars/hour} \]

4. Calculate his pay for the next paycheck with the new rate:
   His pay with the new rate over four weeks will be: \[ 14 \text{ hours} \times 8.25 \text{ dollars/hour} = 115.50 \text{ dollars} \]

Therefore, the amount Aaron will be paid in his next paycheck is D. $115.50.

Answer 2

Jason is saving up for a skateboard and helmet. The skateboard is $45.50 with tax and the helmet is $18.25 with tax. He earned 1/3

of the money by mowing lawns and the rest by babysitting. How much did Jason earn babysitting?

A.

$19.13

B.

$21.25

C.

$30.33

D.

$42.50

Answer 3

To determine how much Jason earned babysitting, we first need to calculate the total cost of the skateboard and helmet, and then find the portion he earned from babysitting.

1. Calculate the total cost of the skateboard and helmet: \[ \text{Cost of skateboard} = 45.50 \text{ dollars} \] \[ \text{Cost of helmet} = 18.25 \text{ dollars} \] \[ \text{Total cost} = 45.50 + 18.25 = 63.75 \text{ dollars} \]

2. Calculate the amount Jason earned by mowing lawns: He earned 1/3 of the total amount by mowing lawns: \[ \text{Amount earned from mowing} = \frac{1}{3} \times 63.75 = 21.25 \text{ dollars} \]

3. Calculate the amount earned by babysitting: The rest of the money he earned comes from babysitting, which can be calculated as: \[ \text{Amount earned from babysitting} = \text{Total cost} - \text{Amount earned from mowing} \] \[ \text{Amount earned from babysitting} = 63.75 - 21.25 = 42.50 \text{ dollars} \]

Therefore, the amount Jason earned babysitting is D. $42.50.

Answer 4

1/2 x 4/3 + 5/6 Divided by 7/8

Answer 5

To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we need to break it down step by step.

Step 1: Calculate \( \frac{1}{2} \times \frac{4}{3} \)

\[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \quad (\text{after simplifying by dividing the numerator and denominator by 2}) \]

Step 2: Calculate \( \frac{5}{6} \div \frac{7}{8} \)

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \times 8}{6 \times 7} = \frac{40}{42} = \frac{20}{21} \quad (\text{after simplifying by dividing both by 2}) \]

Step 3: Add the two results from Step 1 and Step 2

Now we will add \( \frac{2}{3} + \frac{20}{21} \). To do this, 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 we can add:

\[ \frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21} \]

Final Result

The final answer is:

\[ \frac{34}{21} \]

This can also be expressed as:

\[ 1 \frac{13}{21} \]

So, the result of the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \) is \( \frac{34}{21} \) or \( 1 \frac{13}{21} \).

Answer 6

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 7

To determine which combination of snacks Rashad could purchase with his remaining $17, we need to calculate the total cost of each option provided and see if it fits his budget.

Snack Prices:

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

Now, we will calculate the total cost for each option:

Option A: 2 drinks and 3 popcorns

• Cost of 2 drinks: \[ 2 \times 2.75 = 5.50 \]
• Cost of 3 popcorns: \[ 3 \times 4.00 = 12.00 \]
• Total cost: \[ 5.50 + 12.00 = 17.50 \]

Option B: 3 popcorns and 3 candies

• Cost of 3 popcorns: \[ 3 \times 4.00 = 12.00 \]
• Cost of 3 candies: \[ 3 \times 1.50 = 4.50 \]
• Total cost: \[ 12.00 + 4.50 = 16.50 \]

Option C: 4 popcorns and 1 candy

• Cost of 4 popcorns: \[ 4 \times 4.00 = 16.00 \]
• Cost of 1 candy: \[ 1 \times 1.50 = 1.50 \]
• Total cost: \[ 16.00 + 1.50 = 17.50 \]

Option D: 4 drinks and 2 popcorns

• Cost of 4 drinks: \[ 4 \times 2.75 = 11.00 \]
• Cost of 2 popcorns: \[ 2 \times 4.00 = 8.00 \]
• Total cost: \[ 11.00 + 8.00 = 19.00 \]

Summary of Total Costs:

• Option A: $17.50 (over budget)
• Option B: $16.50 (within budget)
• Option C: $17.50 (over budget)
• Option D: $19.00 (over budget)

Conclusion:

The only combination Rashad could purchase with his remaining $17 is B. 3 popcorns and 3 candies, which costs $16.50.

Answer 8

8x+3(x+5)-5(x-4)

Answer 9

To simplify the expression \( 8x + 3(x + 5) - 5(x - 4) \), let's start by distributing the terms inside the parentheses.

Step 1: Distribute \(3\) and \(-5\)

1. Distributing \(3\) in \(3(x + 5)\): \[ 3(x + 5) = 3x + 15 \]

2. Distributing \(-5\) in \(-5(x - 4)\): \[ -5(x - 4) = -5x + 20 \]

Step 2: Substitute back into the expression

Now substitute these expanded terms back into the original expression: \[ 8x + (3x + 15) + (-5x + 20) \]

Step 3: Combine like terms

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

So the expression simplifies to: \[ 6x + 35 \]

Final Result

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

Answer 10

Jackson is given the expression below to simplify.

9x – 4 + 4x + 5x + 19

Which expression is equivalent to Jackson's expression?

A.

3(6x + 5)

B.

18x + 23

C.

5(x + 2)

D.

14x + 19

Answer 11

To simplify the expression \(9x - 4 + 4x + 5x + 19\), we will combine like terms step by step.

Step 1: Combine the \(x\) terms

The \(x\) terms in the expression are \(9x\), \(4x\), and \(5x\). \[ 9x + 4x + 5x = 18x \]

Step 2: Combine the constant terms

The constant terms in the expression are \(-4\) and \(19\). \[ -4 + 19 = 15 \]

Step 3: Write the simplified expression

Combining the results from Steps 1 and 2, we have: \[ 18x + 15 \]

Step 4: Check the answer choices against the simplified expression

Now, we'll check which of the options is equivalent to \(18x + 15\):

A. \(3(6x + 5) = 3 \cdot 6x + 3 \cdot 5 = 18x + 15\) (This is a match)

B. \(18x + 23\) (This does not match)

C. \(5(x + 2) = 5x + 10\) (This does not match)

D. \(14x + 19\) (This does not match)

Final Result

The expression equivalent to Jackson's expression is: A. \(3(6x + 5)\).