The big can held 18 ounces and cost $$ \$ 2.52 $$. The small can held only 12 ounces and cost $$ \$ 1.08 $$. Find both unit prices. Which can was the better buy?

Question

UpStudy AI · Accepted Answer

To find the unit prices for both the big can and the small can, we will follow these steps:

1. **Calculate the unit price for the big can.**
   - The big can holds 18 ounces and costs $$ \$ 2.52 $$.
   - The unit price is calculated by dividing the total cost by the total ounces.

$$
   \text{Unit Price (Big Can)} = \frac{\text{Cost}}{\text{Ounces}} = \frac{2.52}{18}
   $$

2. **Calculate the unit price for the small can.**
   - The small can holds 12 ounces and costs $$ \$ 1.08 $$.
   - Similarly, we calculate the unit price.

$$
   \text{Unit Price (Small Can)} = \frac{\text{Cost}}{\text{Ounces}} = \frac{1.08}{12}
   $$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1.08}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{27}{25}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{27}{25}\times \frac{1}{12}$$
- step3: Reduce the numbers:
  $$\frac{9}{25}\times \frac{1}{4}$$
- step4: Multiply the fractions:
  $$\frac{9}{25\times 4}$$
- step5: Multiply:
  $$\frac{9}{100}$$
Calculate or simplify the expression $$ 2.52/18 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2.52}{18}$$
- step1: Convert the expressions:
  $$\frac{\frac{63}{25}}{18}$$
- step2: Multiply by the reciprocal:
  $$\frac{63}{25}\times \frac{1}{18}$$
- step3: Reduce the numbers:
  $$\frac{7}{25}\times \frac{1}{2}$$
- step4: Multiply the fractions:
  $$\frac{7}{25\times 2}$$
- step5: Multiply:
  $$\frac{7}{50}$$
The calculations for the unit prices are as follows:

1. **Unit Price for the Big Can:**
   $$
   \text{Unit Price (Big Can)} = \frac{2.52}{18} = 0.14
   $$
   This means the unit price for the big can is $$ \$ 0.14 $$ per ounce.

2. **Unit Price for the Small Can:**
   $$
   \text{Unit Price (Small Can)} = \frac{1.08}{12} = 0.09
   $$
   This means the unit price for the small can is $$ \$ 0.09 $$ per ounce.

### Conclusion:
- The unit price for the big can is $$ \$ 0.14 $$ per ounce.
- The unit price for the small can is $$ \$ 0.09 $$ per ounce.

Since $$ 0.09 < 0.14 $$, the small can is the better buy.
The big can costs \$0.14 per ounce, and the small can costs \$0.09 per ounce. The small can is the better buy.

The big can held 18 ounces and cost \( \$ 2.52 \). The small can held only 12 ounces and cost \( \$ 1.08 \). Find both unit prices. Which can was the better buy?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Arithmetic Questions