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Answer :
Alright, let's break this problem down step by step:
1. Understanding the Problem:
- The supplier sells [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch for every [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel.
- The total weight of mulch and gravel combined is 172 pounds.
- We need to find out how many pounds of each item (mulch and gravel) the supplier sells.
2. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch can be converted to a decimal:
[tex]\[
2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25
\][/tex]
- [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel can be converted to a decimal:
[tex]\[
1 \frac{1}{3} = 1 + \frac{1}{3} = 1.333333333\ldots \approx 1.33
\][/tex]
3. Calculate the Combined Weight of One Unit:
- Add the weight of the mulch and gravel for one unit to get the total weight of one unit:
[tex]\[
\text{Unit weight} = 2.25 + 1.33 = 3.58
\][/tex]
4. Calculate the Total Number of Units:
- Divide the total weight by the weight of one unit to find out how many such units make up 172 pounds:
[tex]\[
\text{Number of units} = \frac{172}{3.58} \approx 48
\][/tex]
5. Calculate Weight of Each Item:
- Now, multiply the number of units by the weight of mulch per unit to get the total weight of mulch:
[tex]\[
\text{Weight of mulch} = 48 \times 2.25 = 108 \text{ pounds}
\][/tex]
- Similarly, multiply the number of units by the weight of gravel per unit to get the total weight of gravel:
[tex]\[
\text{Weight of gravel} = 48 \times 1.33 = 64 \text{ pounds}
\][/tex]
6. Conclusion:
- The supplier sells 108 pounds of mulch and 64 pounds of gravel.
So, the supplier sells 108 pounds of mulch and 64 pounds of gravel.
1. Understanding the Problem:
- The supplier sells [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch for every [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel.
- The total weight of mulch and gravel combined is 172 pounds.
- We need to find out how many pounds of each item (mulch and gravel) the supplier sells.
2. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch can be converted to a decimal:
[tex]\[
2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25
\][/tex]
- [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel can be converted to a decimal:
[tex]\[
1 \frac{1}{3} = 1 + \frac{1}{3} = 1.333333333\ldots \approx 1.33
\][/tex]
3. Calculate the Combined Weight of One Unit:
- Add the weight of the mulch and gravel for one unit to get the total weight of one unit:
[tex]\[
\text{Unit weight} = 2.25 + 1.33 = 3.58
\][/tex]
4. Calculate the Total Number of Units:
- Divide the total weight by the weight of one unit to find out how many such units make up 172 pounds:
[tex]\[
\text{Number of units} = \frac{172}{3.58} \approx 48
\][/tex]
5. Calculate Weight of Each Item:
- Now, multiply the number of units by the weight of mulch per unit to get the total weight of mulch:
[tex]\[
\text{Weight of mulch} = 48 \times 2.25 = 108 \text{ pounds}
\][/tex]
- Similarly, multiply the number of units by the weight of gravel per unit to get the total weight of gravel:
[tex]\[
\text{Weight of gravel} = 48 \times 1.33 = 64 \text{ pounds}
\][/tex]
6. Conclusion:
- The supplier sells 108 pounds of mulch and 64 pounds of gravel.
So, the supplier sells 108 pounds of mulch and 64 pounds of gravel.
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