Respuesta :
Answer:
5 gallons of soil that contains 30% clay and 5 gallons of soil that contains 70% clay is combined
Step-by-step explanation:
Given:
Soil that contains 30% clay is added to soil that contains 70% clay to create 10 gallons of soil containing 50% clay.
Now, to find the quantity of each of the soils was combined.
Total quantity of soil containing 50% clay = 10 gallons.
Let the quantity of soil that contains 30% clay be [tex]x.[/tex]
And let the quantity of soil that contains 70% clay be [tex]10-x.[/tex]
Now, to get the quantity of soils:
[tex]30\%\ of\ x+70\%\ of\ (10-x)=50\%\ of\ 10[/tex]
[tex]\frac{30}{100} \times x+\frac{70}{100} \times (10-x)=\frac{50}{100} \times 10[/tex]
[tex]0.30x+0.70(10-x)=5[/tex]
[tex]0.30x+7-0.7x=5[/tex]
[tex]7-0.4x=5[/tex]
Subtracting both sides by 7 we get:
[tex]-0.4x=-2[/tex]
Dividing both sides by -0.4 we get:
[tex]x=5.[/tex]
The quantity of soil that contains 30% clay = 5 gallons.
Now, substituting the value of [tex]x[/tex] we get:
[tex]10-x\\\\=10-5\\\\=5.[/tex]
The quantity of soil that contains 70% clay = 5 gallons.
Therefore, 5 gallons of soil that contains 30% clay and 5 gallons of soil that contains 70% clay is combined.
