TRY IT
YOURSELF
(a) The masses of 2 bags of sugar, and , are 750 g and respectively.
Find the ratio of the mass of to the mass of .

Ask by Tyler Reed. in Indonesia

Jan 23,2025

Question

TRY IT YOURSELF (a) The masses of 2 bags of sugar, $$ A $$ and $$ B $$, are 750 g and $$ 1 \frac{1}{3} \mathrm{~kg} $$ respectively. Find the ratio of the mass of $$ B $$ to the mass of $$ A $$.

UpStudy AI · Accepted Answer

To find the ratio of the mass of bag $$ B $$ to the mass of bag $$ A $$, follow these steps:

1. **Convert Units to the Same Measure:**
   
   - **Mass of Bag $$ A $$:** $$ 750 $$ grams (already in grams).
   - **Mass of Bag $$ B $$:** $$ 1 \frac{1}{3} $$ kilograms.
     
     Convert kilograms to grams:
     $$
     1 \, \text{kg} = 1000 \, \text{grams}
     $$
     $$
     1 \frac{1}{3} \, \text{kg} = \frac{4}{3} \, \text{kg} = \frac{4}{3} \times 1000 \, \text{grams} = 1333.\overline{3} \, \text{grams}
     $$

2. **Set Up the Ratio:**
   
   The ratio of the mass of $$ B $$ to $$ A $$ is:
   $$
   \text{Mass of } B : \text{Mass of } A = 1333.\overline{3} \, \text{g} : 750 \, \text{g}
   $$

3. **Simplify the Ratio:**
   
   To simplify the ratio, it's easier to eliminate the decimal by multiplying both terms by 3:
   $$
   1333.\overline{3} \times 3 = 4000 \, \text{g}
   $$
   $$
   750 \times 3 = 2250 \, \text{g}
   $$
   Now, the ratio is:
   $$
   4000 : 2250
   $$
   
   Divide both numbers by their greatest common divisor (which is 250):
   $$
   \frac{4000}{250} : \frac{2250}{250} = 16 : 9
   $$

4. **Final Answer:**
   
   The ratio of the mass of $$ B $$ to the mass of $$ A $$ is **16:9**.

**Answer:**  
After simplifying, the ratio of mass B to mass A is 16 to 9.
The ratio of the mass of bag $$ B $$ to bag $$ A $$ is **16:9**.

TRY IT
YOURSELF
(a) The masses of 2 bags of sugar, and , are 750 g and respectively.
Find the ratio of the mass of to the mass of .

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TRY IT YOURSELF (a) The masses of 2 bags of sugar, and , are 750 g and respectively. Find the ratio of the mass of to the mass of .