Question

Mr. Imani wants to purchase paper and notebooks for his classroom. At Dollar Discount he can buy packs of paper, p , for $1.25 each and notebooks, n , for $2.50 each. This is modeled by 1.25p + 2.50n . Evaluate for p = 10 and n=30 to find how much it will cost Mr. Imani to purchase 10 packs of paper and 30 notebooks.

Answer 1

To calculate the total cost for Mr. Imani to purchase 10 packs of paper and 30 notebooks, we can use the given cost formula:

\[ \text{Total Cost} = 1.25p + 2.50n \]

Substituting the values \( p = 10 \) and \( n = 30 \):

\[ \text{Total Cost} = 1.25(10) + 2.50(30) \]

Calculating each term:

1. Calculate \( 1.25 \times 10 \): \[ 1.25 \times 10 = 12.50 \]

2. Calculate \( 2.50 \times 30 \): \[ 2.50 \times 30 = 75.00 \]

Now, add the two results together:

\[ \text{Total Cost} = 12.50 + 75.00 = 87.50 \]

Thus, the total cost for Mr. Imani to purchase 10 packs of paper and 30 notebooks is $87.50.

Answer 2

The formula for finding the volume of a square prism is s2h , where s is the length of each side of the square base and h is the height of the prism. Evaluate to find the volume given values of s = 4 and h = 6 .

Answer 3

To find the volume of a square prism using the formula \( V = s^2 h \), we can substitute the given values \( s = 4 \) and \( h = 6 \).

1. First, calculate \( s^2 \): \[ s^2 = 4^2 = 16 \]

2. Now, multiply \( s^2 \) by \( h \): \[ V = 16 \times 6 \]

3. Calculate the result: \[ V = 96 \]

Thus, the volume of the square prism is 96 cubic units.

Answer 4

Each month Ms. Tanaka is paid a base salary of $2,500 in addition to $100 for each television that she sells. This is modeled by 2,500 + 100t , where t represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.

Answer 5

To calculate Ms. Tanaka's earnings for selling 12 televisions, we can use the given formula:

\[ \text{Earnings} = 2,500 + 100t \]

Substituting \( t = 12 \):

\[ \text{Earnings} = 2,500 + 100(12) \]

Now, calculate \( 100 \times 12 \):

\[ 100 \times 12 = 1,200 \]

Next, add this amount to her base salary:

\[ \text{Earnings} = 2,500 + 1,200 = 3,700 \]

Therefore, Ms. Tanaka will earn $3,700 for selling 12 televisions this month.

Answer 6

Robert is preparing a poster-board presentation. He wants to make a decorative pattern with 10 squares to fill part of the poster. The area of the poster board is 720 square inches. To find how much space Robert will have left for his presentation if he uses squares with 7-inch sides, evaluate 720 − 10s2 when s = 7 .

Answer 7

To find out how much space Robert will have left for his presentation after using the squares, we can use the formula:

\[ \text{Remaining Space} = 720 - 10s^2 \]

where \( s \) is the length of the side of each square. Given that \( s = 7 \):

1. First, calculate \( s^2 \): \[ s^2 = 7^2 = 49 \]

2. Now, multiply \( s^2 \) by 10: \[ 10s^2 = 10 \times 49 = 490 \]

3. Subtract this value from the total area of the poster board: \[ \text{Remaining Space} = 720 - 490 \]

4. Calculate the remaining space: \[ \text{Remaining Space} = 230 \]

Therefore, Robert will have 230 square inches of space left for his presentation after using the squares.

Answer 8

Mr. Rodriguez has a vegetable garden that borders his house. He wants to put a fence around it. It costs $7 per yard for the materials. Evaluate 7(l + 2w) , where l is the length and w is the width of his garden, to find the cost for a garden that has a length of 5 yards and a width of 2 yards.

Answer 9

To find the cost of fencing Mr. Rodriguez's vegetable garden, we will use the formula:

\[ \text{Cost} = 7(l + 2w) \]

where \( l \) is the length and \( w \) is the width of the garden. Given that \( l = 5 \) yards and \( w = 2 \) yards, we can substitute these values into the formula.

1. Substitute \( l \) and \( w \): \[ \text{Cost} = 7(5 + 2 \times 2) \]

2. Calculate \( 2 \times 2 \): \[ 2 \times 2 = 4 \]

3. Substitute this back into the equation: \[ \text{Cost} = 7(5 + 4) \]

4. Now, calculate \( 5 + 4 \): \[ 5 + 4 = 9 \]

5. Now multiply by 7: \[ \text{Cost} = 7 \times 9 = 63 \]

Therefore, the cost to put a fence around Mr. Rodriguez's vegetable garden is $63.