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Math  /  Numbers & Operations

Question2. Ethan buys a pair of jeans online for $22\$ 22. After the shipping charge is added, the new total is $25.52\$ 25.52. What is the percent increase in the cost of the jeans due to the shipping charge?
3. A restaurant manager decides to decrease the size of the soft drink cups by 10%10 \%. The new drink cup holds 27 ounces. How much did the original cup hold?
In July, Noor's family used 12,568 gallons of water. In August, they used 11,562 gallons fater. What is the percent decrease in the family's water usage? Round your answer to earest percent.

Studdy Solution

STEP 1

1. The original cost of the jeans is $22 \$22 .
2. The total cost after adding the shipping charge is $25.52 \$25.52 .
3. We need to find the percent increase due to the shipping charge.

STEP 2

1. Calculate the shipping charge.
2. Calculate the percent increase.
3. 1. Set up an equation to represent the decrease.
2. Solve for the original size.
STEP_1: High_Level_Step: 1 Let x x be the original size of the cup. The new size is 90% 90\% of the original size.
0.9x=270.9x = 27
High_Level_Step_Completed: TRUE
STEP_2: High_Level_Step: 2 Solve for x x by dividing both sides by 0.9 0.9 .
x=270.9=30x = \frac{27}{0.9} = 30
High_Level_Step_Completed: TRUE
The original cup held 30 \boxed{30} ounces.
### Problem 4: Percent Decrease in Water Usage
_ASSUMPTIONS_:
1. Water usage in July was 12,568 gallons.
2. Water usage in August was 11,562 gallons.
4. We need to find the percent decrease in water usage.
_HIGH_LEVEL_APPROACH_:
1. Calculate the decrease in water usage.
2. Calculate the percent decrease.
STEP_1: High_Level_Step: 1 Calculate the decrease in water usage by subtracting August usage from July usage.
Decrease=12,568−11,562=1,006 gallons\text{Decrease} = 12,568 - 11,562 = 1,006 \text{ gallons}
High_Level_Step_Completed: TRUE
STEP_2: High_Level_Step: 2 Calculate the percent decrease using the formula:
Percent Decrease=(DecreaseJuly Usage)×100\text{Percent Decrease} = \left(\frac{\text{Decrease}}{\text{July Usage}}\right) \times 100
Substitute the known values:
Percent Decrease=(1,00612,568)×100≈8%\text{Percent Decrease} = \left(\frac{1,006}{12,568}\right) \times 100 \approx 8\%
High_Level_Step_Completed: TRUE
The percent decrease in the family's water usage is approximately 8% \boxed{8\%} .

STEP 3

Calculate the shipping charge by subtracting the original cost from the total cost.
Shipping Charge=$25.52−$22=$3.52\text{Shipping Charge} = \$25.52 - \$22 = \$3.52

STEP 4

Calculate the percent increase using the formula:
Percent Increase=(Shipping ChargeOriginal Cost)×100\text{Percent Increase} = \left(\frac{\text{Shipping Charge}}{\text{Original Cost}}\right) \times 100
Substitute the known values:
Percent Increase=(3.5222)×100≈16%\text{Percent Increase} = \left(\frac{3.52}{22}\right) \times 100 \approx 16\%
The percent increase in the cost of the jeans due to the shipping charge is approximately 16% \boxed{16\%} .
### Problem 3: Original Size of the Soft Drink Cup
_ASSUMPTIONS_:
1. The size of the new drink cup is 27 ounces.
2. The size of the cup was decreased by 10% 10\% .
3. We need to find the original size of the cup.

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