A chemical company makes 2 brands of antifreeze.the first brand is 30%pure antifreeze and the second brand is 55%pure antifreeze.in order to obtain 170 gallons of a mixture that contains 35% pure antifreeze how many gallons of each brand antifreeze must be used

Answer 1

To solve this problem, we can set up a system of equations.

Let x be the number of gallons of brand 1 antifreeze (30% pure).
Let y be the number of gallons of brand 2 antifreeze (55% pure).

We are given the following information:
1. We need to obtain 170 gallons of a mixture that contains 35% pure antifreeze.

This information can be expressed in the following equation:
x + y = 170 (equation 1)

2. Brand 1 antifreeze is 30% pure and brand 2 antifreeze is 55% pure.

To obtain a mixture that contains 35% pure antifreeze, we can use the weighted average formula:
(30% * x + 55% * y) / (x + y) = 35% (equation 2)

Now, we can solve the system of equations.

Substitute equation 1 into equation 2:
(30% * x + 55% * y) / 170 = 35%

Multiply both sides by 170 to eliminate the fraction:
30% * x + 55% * y = 35% * 170

Simplify:
0.3x + 0.55y = 0.35 * 170

Multiply 0.35 by 170:
0.3x + 0.55y = 59.5 (equation 3)

Now, we have a system of two equations:
x + y = 170 (equation 1)
0.3x + 0.55y = 59.5 (equation 3)

We can solve this system of equations through substitution, elimination, or other methods.

Let's solve by substitution:
Solve equation 1 for x:
x = 170 - y

Substitute this value of x into equation 3:
0.3(170 - y) + 0.55y = 59.5

Distribute:
51 - 0.3y + 0.55y = 59.5

Combine like terms:
0.25y = 8.5

Divide by 0.25:
y = 34

Now, substitute this value of y back into equation 1 to solve for x:
x + 34 = 170
x = 136

Therefore, we need 136 gallons of brand 1 antifreeze and 34 gallons of brand 2 antifreeze to obtain a mixture of 170 gallons that contains 35% pure antifreeze.

Answer 2

Divide
9ay/2y^4 /3a/4y
Simply as much as possible

Answer 3

To divide the expression (9ay/2y^4) by (3a/4y), we can simplify by following these steps:

First, let's write down the expression:

(9ay/2y^4) / (3a/4y)

To divide fractions, we keep the first fraction as it is and change the division sign to multiplication. Then, we take the reciprocal of the second fraction. Therefore, the expression becomes:

(9ay/2y^4) * (4y/3a)

Now, let's simplify by canceling out common factors.

The 2 in the numerator cancels out with the 2 in the denominator:

(9ay/(1y^4)) * (4y/3a)

Next, we can simplify the variables:

9ay * 4y / 1y^4 / 3a

Combining like terms, we have:

36ay^2 / 1y^4 / 3a

To divide fractions in the denominator, we multiply by the reciprocal:

36ay^2 * 3a / 1y^4

Multiply the numerators and denominators:

(36ay^2 * 3a) / (1 * 1y^4)

Simplify further:

108a^2y^2 / y^4

Using the laws of exponents, we can simplify y^2 in the numerator and denominator:

108a^2 / y^(4-2)

Simplifying further, we get:

108a^2 / y^2

Therefore, the simplified expression is 108a^2 / y^2.