You should use 2.8 ft of soil with 35% clay and 7.2 ft of soil with 10% clay
Step-by-step explanation:
To build the garden of your dreams you need
1. 10 ft of soil containing 17% clay
2. You have two types of soil you can combine to achieve this
3. soil with 35% clay and soil with 10% clay
We need to find how much of each soil you should use
Let us represent these information in two equations of two variables
Assume that you will use x ft from soil with 35% clay and y ft from
soil with 10% clay
∵ You need 10 feet to build the garden
∴ x + y = 10 ⇒ (1)
∵ x has 35% of clay
∴ The clay = 35% x = (35/100)x = 0.35 x
∵ y has 10% of clay
∴ The clay = 10% y = (10/100)x = 0.10 y
∵ The 10 feet of soil containing 17% of clay
∴ The clay = 17% of 10 = (17/100)(10) = 1.70
∴ 0.35 x + 0.10 y = 1.70 ⇒ (2)
Now we have system of equations let us solve them
∵ x + y = 10 ⇒ (1)
∵ 0.35 x + 0.10 y = 1.70 ⇒ (2)
- Multiply equation (1) by -0.10
∴ -0.10 x - 0.10 y = -1 ⇒ (3)
- Add equations (2) and (3)
∴ 0.25 x = 0.70
- Divide both sides by 0.25
∴ x = 2.8
- Substitute the value of x in equation (1)
∴ 2.8 + y = 10
- Subtract 2.8 from both sides
∴ y = 7.2
∴ The amount of soil with 35% clay is 2.8 ft
∴ The amount of soil with 10% clay is 7.2 ft
You should use 2.8 ft of soil with 35% clay and 7.2 ft of soil with 10% clay
Learn more:
You can learn more about system of equations in brainly.com/question/9045597
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