Which equation is equivalent to 11x - (2-x) = 51
A. 13x = 51
B. 12x = 53
C. 12x = 49
D. 10x = 53
Expanding the equation 11x - (2-x) = 51, we get:
11x - 2 + x = 51
Combining like terms, we have:
12x - 2 = 51
Adding 2 to both sides of the equation:
12x = 53
Therefore, the equivalent equation is:
B. 12x = 53
A company charges $7 for a T-shirt and ships any order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. How many T-shirts did the principal order?
Let's assume the number of T-shirts the principal ordered is represented by x.
The cost of the T-shirts is $7 per T-shirt, so the cost of the T-shirts can be calculated as 7x.
The shipping cost is a fixed $22 for any order.
The total cost of the order is the sum of the cost of the T-shirts and the shipping cost, which is $1,520.
Therefore, the equation is:
7x + 22 = 1520
Subtracting 22 from both sides of the equation:
7x = 1520 - 22
7x = 1498
Dividing both sides of the equation by 7:
x = 1498 / 7
x ≈ 214
Therefore, the principal ordered approximately 214 T-shirts for the school store.
3
48
6
96
144
The table below shows the total number of brake pads produced by machines throughout a 12-hour work day.
Hours Worked
Brake Pads Produced
3 6 9 12
48 96 144 192
What is the unit rate for brake pads produced per hour?
A.
4 brake pads per hour
B.
3 brake pads per hour
C.
12 brake pads per hour
D.
16 brake pads per hour
To find the unit rate for brake pads produced per hour, we divide the total number of brake pads produced by the number of hours worked.
For example, in the first row of the table, the machine produced 48 brake pads in 3 hours. To find the unit rate, we divide 48 by 3:
48 brake pads / 3 hours = 16 brake pads per hour
Following this calculation for each row in the table:
48 brake pads / 3 hours = 16 brake pads per hour
96 brake pads / 6 hours = 16 brake pads per hour
144 brake pads / 9 hours = 16 brake pads per hour
192 brake pads / 12 hours = 16 brake pads per hour
So, the unit rate for brake pads produced per hour is:
D. 16 brake pads per hour
Sam's Fruit Cellar earns a $0.40 profit for each apple that it sells and a $0.40 profit for each banana that it sells. Which expression shows Sam's total profits from selling apples (a) and bananas (b)?
A.
0.40(ab)
B.
0.40(a + b)
C.
0.40 + a + 0.40 + b
D.
0.80(ab)
The expression that shows Sam's total profits from selling apples (a) and bananas (b) is:
B. 0.40(a + b)
This expression represents the sum of the profits from selling apples and the profits from selling bananas.
Eric is baking a cake. The recipe calls for
2 1/2 pounds of flour for every
1/ 4 cup of sugar. How many pounds of flour should Eric use for 1 cup of sugar?
To find out how many pounds of flour Eric should use for 1 cup of sugar, we need to set up a ratio using the given information from the recipe.
The recipe calls for 2 1/2 pounds of flour for every 1/4 cup of sugar.
To make a comparison for 1 cup of sugar, we need to convert the measurement to 1 cup. Since 1 cup is equal to 4 1/4 cups, we can use this ratio:
2 1/2 pounds : 1/4 cup = x pounds : 1 cup
Cross-multiplying the ratio, we get:
(2 1/2 pounds) * (1 cup) = (1/4 cup) * (x pounds)
Simplifying the equation, we have:
2 1/2 cups = (1/4) * x
To solve for x, we can multiply both sides of the equation by 4:
10 cups = x
Therefore, Eric should use 10 pounds of flour for 1 cup of sugar.