Jeremy buys a value pack of cheese crackers that contains 42 1/2

Question

ounces of crackers. He divides this into servings of 1 1/4

ounces each. What is the total number of servings Jeremy can make from the value pack?

A.
8 1/2
servings

B. 34
servings

C.
43 3/4
servings

D. 53
servings

Answer 1

To find the total number of servings Jeremy can make from the value pack of cheese crackers, we need to divide the total amount of crackers by the serving size.

1. Convert the quantities to improper fractions for easier calculation:

   • The total amount of cheese crackers is \( 42 \frac{1}{2} \) ounces. This can be converted to an improper fraction: \[ 42 \frac{1}{2} = \frac{42 \times 2 + 1}{2} = \frac{84 + 1}{2} = \frac{85}{2} \]
   • The serving size is \( 1 \frac{1}{4} \) ounces, which can also be converted to an improper fraction: \[ 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \]

2. Now we can divide the total ounces of crackers by the ounces per serving: \[ \text{Number of servings} = \frac{\frac{85}{2}}{\frac{5}{4}} \]

3. When dividing fractions, we multiply by the reciprocal of the divisor: \[ \frac{85}{2} \div \frac{5}{4} = \frac{85}{2} \times \frac{4}{5} = \frac{85 \times 4}{2 \times 5} = \frac{340}{10} = 34 \]

Therefore, the total number of servings Jeremy can make is 34 servings.

The answer is B. 34 servings.

Answer 2

A hot air balloon leaves the ground and rises to an elevation of 1,100 feet. During the next 30 minutes, it descends 500 feet, rises 950 feet, descends 375 feet, and finally passes over a school. What is the elevation of the balloon when it passes over the school?

A.
1,025 feet

B.
1,100 feet

C.
1,175 feet

D.
1,550 feet

Answer 3

To find the elevation of the hot air balloon when it passes over the school, we can start from its initial elevation and apply the changes in elevation step by step.

1. The balloon rises to 1,100 feet.

2. Then it descends 500 feet: \[ 1,100 - 500 = 600 \text{ feet} \]

3. Next, it rises 950 feet: \[ 600 + 950 = 1,550 \text{ feet} \]

4. Then, it descends 375 feet: \[ 1,550 - 375 = 1,175 \text{ feet} \]

So, when the balloon passes over the school, its elevation is 1,175 feet.

The correct answer is C. 1,175 feet.

Answer 4

Aaron works
3 1/2
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 5

To calculate Aaron's next paycheck after receiving a $1.00 raise, we'll perform the following steps:

1. Calculate the new hourly rate: \[ \text{New hourly rate} = 7.25 + 1.00 = 8.25 , \text{dollars per hour} \]

2. Determine the total hours worked in four weeks:

   • Aaron works \( 3 \frac{1}{2} \) hours every Saturday. We convert this to a decimal: \[ 3 \frac{1}{2} = 3.5 , \text{hours} \]
   • Since Aaron works every Saturday for 4 weeks, the total hours worked over four weeks is: \[ \text{Total hours} = 3.5 \times 4 = 14 , \text{hours} \]

3. Calculate the total pay with the new hourly rate: \[ \text{Total pay} = \text{Total hours} \times \text{New hourly rate} \] \[ \text{Total pay} = 14 \times 8.25 = 115.50 , \text{dollars} \]

Therefore, Aaron will be paid $115.50 in his next paycheck.

The correct answer is D. $115.50.

Answer 6

What is the value of the expression
2/3 (-6 + 4)
?

A.
0

B.
-2/3

C.
4/3

D.
-4/3

Answer 7

To evaluate the expression \( \frac{2}{3} (-6 + 4) \), follow these steps:

1. Calculate the value inside the parentheses: \[ -6 + 4 = -2 \]

2. Now substitute this value back into the expression: \[ \frac{2}{3} \times (-2) \]

3. Multiply: \[ \frac{2 \times (-2)}{3} = \frac{-4}{3} \]

Thus, the value of the expression \( \frac{2}{3} (-6 + 4) \) is \(-\frac{4}{3}\).

The correct answer is D. \(-\frac{4}{3}\).

Answer 8

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 9

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

1. Calculate the total cost of the skateboard and helmet:

   • Cost of skateboard: $45.50
   • Cost of helmet: $18.25
   • Total cost: \[ \text{Total cost} = 45.50 + 18.25 = 63.75 \]

2. Determine how much Jason earned by mowing lawns:

   • Jason earned \( \frac{1}{3} \) of the total amount: \[ \text{Earnings from mowing lawns} = \frac{1}{3} \times 63.75 = 21.25 \]

3. Calculate how much Jason earned babysitting:

   • The amount he earned babysitting is the remainder of the total cost: \[ \text{Earnings from babysitting} = \text{Total cost} - \text{Earnings from mowing lawns} \] \[ \text{Earnings from babysitting} = 63.75 - 21.25 = 42.50 \]

Therefore, Jason earned $42.50 babysitting.

The correct answer is D. $42.50.

Answer 10

Which expression results in a negative number?
A.
1/2 ( -2 x 2/5)


B.
1/3 (-18) / -3

C.
-1/4 (-7 -6)

D.
-1/2 / -2/3

Answer 11

Let's evaluate each option to determine which expression results in a negative number.

A. \( \frac{1}{2} (-2 \times \frac{2}{5}) \)

Calculate the inner part: \[ -2 \times \frac{2}{5} = -\frac{4}{5} \] Now multiply by \(\frac{1}{2}\): \[ \frac{1}{2} \times -\frac{4}{5} = -\frac{4}{10} = -\frac{2}{5} \] This expression is negative.

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B. \( \frac{1}{3} (-18) / -3 \)

Start with: \[ \frac{1}{3} \times -18 = -6 \] Now divide by \(-3\): \[ -6 / -3 = 2 \] This expression is positive.

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C. \( -\frac{1}{4} (-7 - 6) \)

Calculate the inner part: \[ -7 - 6 = -13 \] Now multiply: \[ -\frac{1}{4} \times -13 = \frac{13}{4} \] This expression is positive.

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D. \( -\frac{1}{2} / -\frac{2}{3} \)

Dividing a negative by a negative gives a positive: \[ -\frac{1}{2} \div -\frac{2}{3} = -\frac{1}{2} \times -\frac{3}{2} = \frac{3}{4} \] This expression is positive.

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Conclusion: The expression that results in a negative number is:

A. \( \frac{1}{2} (-2 \times \frac{2}{5}) \) which simplifies to \(-\frac{2}{5}\).