could someone please check these problems for me?
thank you!
1. Soybean meal is 16% protein; cornmeal is 8% protein. How many lbs of each should be mixed together in order to get 320 lb mixture that is 9% protein/
A: cornmeal- 40lbs
soybean-280 lbs
2. -0.7x<-35
A: x>50
3. 2+4x<14
A: x<3
4. 8x-(2x+8)=34
A:x=7
5. 5/4x+1/8x=11/8+x
A:x=11/3
1. Correct
2. Correct
3. Correct
4. Correct
5. Correct
They're all right. Good job!
thats like exactly what we are hittin up in algebraa
Soybean meal is 16% protein: cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lib mixture that is 15% protein?
Sure, let's go through each problem one by one.
1. Soybean meal is 16% protein, while cornmeal is 8% protein. We need to find the amounts of each ingredient to get a 320 lb mixture that is 9% protein.
Let's assume x lbs of soybean meal and y lbs of cornmeal.
The total weight of the mixture is x + y = 320 lbs.
The protein content equation is (0.16 * x + 0.08 * y) / 320 = 0.09.
To simplify the equation, multiply both sides by 320: 0.16 * x + 0.08 * y = 0.09 * 320.
Now, we have a system of two equations:
x + y = 320 ...(1)
0.16 * x + 0.08 * y = 0.09 * 320 ...(2)
There are several ways to solve this system of equations. One way is to use substitution or elimination.
Using substitution, solve equation (1) for x: x = 320 - y.
Substitute this value of x into equation (2):
0.16 * (320 - y) + 0.08 * y = 0.09 * 320.
Now, you can solve for y:
51.2 - 0.16 * y + 0.08 * y = 28.8,
-0.08 * y = -22.4,
y = 280 lbs.
Substituting this value back into equation (1), we find:
x + 280 = 320,
x = 40 lbs.
So, you should mix 280 lbs of soybean meal and 40 lbs of cornmeal to get a 320 lb mixture that is 9% protein.
2. The inequality is -0.7x < -35.
To solve for x, divide both sides of the inequality by -0.7. Keep in mind that dividing by a negative number reverses the inequality.
(-0.7x) / -0.7 > (-35) / -0.7,
x > 50.
Therefore, the solution is x > 50.
3. The inequality is 2 + 4x < 14.
To solve for x, subtract 2 from both sides of the inequality:
2 + 4x - 2 < 14 - 2,
4x < 12.
Next, divide both sides by 4:
(4x) / 4 < 12 / 4,
x < 3.
Thus, the solution is x < 3.
4. The equation is 8x - (2x + 8) = 34.
Start by simplifying the equation:
8x - 2x - 8 = 34,
6x - 8 = 34.
Next, add 8 to both sides of the equation:
6x - 8 + 8 = 34 + 8,
6x = 42.
Now, divide both sides by 6:
(6x) / 6 = 42 / 6,
x = 7.
So, the solution is x = 7.
5. The equation is (5/4)x + (1/8)x = (11/8) + x.
To solve for x, begin by getting rid of the fractions. We can do this by finding a common denominator. In this case, the common denominator is 8.
Multiply each term by 8 to clear the fractions:
8 * (5/4)x + 8 * (1/8)x = 8 * (11/8) + 8 * x.
Simplifying both sides gives:
10x + x = 11 + 8x.
Combine like terms on both sides:
11x = 11 + 8x.
Next, subtract 8x from both sides:
11x - 8x = 11.
Combine like terms again:
3x = 11.
Finally, divide both sides by 3:
(3x) / 3 = 11 / 3.
The solution is x = 11/3, or x ≈ 3.67.
I hope this helps! Let me know if you have any further questions.