Answer :
Sure, let's work through the problem step-by-step:
First, we need to understand the relationship between the mulch and the gravel. The supplier sells:
- [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch for every [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel.
To make calculations easier, we'll convert these mixed numbers to improper fractions and then to decimals:
- [tex]\( 2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25 \)[/tex]
- [tex]\( 1 \frac{1}{3} = 1 + \frac{1}{3} = 1.3333 \)[/tex]
Given that the combined weight of mulch and gravel is 172 pounds, let's define:
- [tex]\( x \)[/tex] = pounds of gravel
- [tex]\( y \)[/tex] = pounds of mulch
From the information above, we know:
1. [tex]\( y = 2.25x \)[/tex]
2. [tex]\( x + y = 172 \)[/tex]
Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x + 2.25x = 172 \][/tex]
[tex]\[ 3.25x = 172 \][/tex]
Next, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{172}{3.25} \][/tex]
[tex]\[ x = 52.92307692307692 \][/tex]
This is the number of pounds of gravel.
Now, calculate [tex]\( y \)[/tex] using the first equation:
[tex]\[ y = 2.25 \times 52.92307692307692 \][/tex]
[tex]\[ y = 119.07692307692307 \][/tex]
So, the supplier sells:
- Approximately 52.92 pounds of gravel
- Approximately 119.08 pounds of mulch
These are the weights of gravel and mulch respectively, based on the given conditions.
First, we need to understand the relationship between the mulch and the gravel. The supplier sells:
- [tex]\( 2 \frac{1}{4} \)[/tex] pounds of mulch for every [tex]\( 1 \frac{1}{3} \)[/tex] pounds of gravel.
To make calculations easier, we'll convert these mixed numbers to improper fractions and then to decimals:
- [tex]\( 2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25 \)[/tex]
- [tex]\( 1 \frac{1}{3} = 1 + \frac{1}{3} = 1.3333 \)[/tex]
Given that the combined weight of mulch and gravel is 172 pounds, let's define:
- [tex]\( x \)[/tex] = pounds of gravel
- [tex]\( y \)[/tex] = pounds of mulch
From the information above, we know:
1. [tex]\( y = 2.25x \)[/tex]
2. [tex]\( x + y = 172 \)[/tex]
Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x + 2.25x = 172 \][/tex]
[tex]\[ 3.25x = 172 \][/tex]
Next, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{172}{3.25} \][/tex]
[tex]\[ x = 52.92307692307692 \][/tex]
This is the number of pounds of gravel.
Now, calculate [tex]\( y \)[/tex] using the first equation:
[tex]\[ y = 2.25 \times 52.92307692307692 \][/tex]
[tex]\[ y = 119.07692307692307 \][/tex]
So, the supplier sells:
- Approximately 52.92 pounds of gravel
- Approximately 119.08 pounds of mulch
These are the weights of gravel and mulch respectively, based on the given conditions.
