QuestionMix 100 pints of liquids A (10% acid), B (40% acid), and C (60% acid) for 45% acid. Find pints of each liquid.

Studdy Solution

STEP 1

Assumptions1. The total volume of the mixture is100 pints. . Liquid A contains10% acid, liquid B contains40% acid, and liquid C contains60% acid.
3. The volume of liquid A is twice the volume of liquid B.
4. The total mixture contains45% acid.

STEP 2

Let's denote the volume of liquid A as $2x$ , the volume of liquid B as $x$ , and the volume of liquid C as $y$ . We can write the equation for the total volume of the mixture as follows $2x + x + y =100$

STEP 3

The total acid in the mixture is the sum of the acid in each of the liquids. We can write the equation for the total acid in the mixture as follows $0.1(2x) +0.x +0.6y =0.45(100)$

STEP 4

implify the equationsFrom the total volume equation, we get $3x + y =100$ From the total acid equation, we get $0.2x +0.4x +0.6y =45$

STEP 5

Multiply the second equation by10 to get rid of the decimal points $2x +4x +y =450$

STEP 6

implify the equation to get $6x +6y =450$

STEP 7

Divide the entire equation by6 to simplify $x + y =75$

STEP 8

Now we have a system of two equations $3x + y =100$ $x + y =75$

STEP 9

Subtract the second equation from the first to find the value of $x$ $2x =25$

STEP 10

olve for $x$ $x =12.5$

STEP 11

Substitute $x =.5$ into the equation $x + y =75$ to find the value of $y$ $.5 + y =75$

STEP 12

olve for $y$ $y =75 -12.5 =62.5$

STEP 13

Substitute $x =12.5$ into the equation $2x = A$ to find the volume of liquid A $A =2 \times12.5 =25$ So, we need25 pints of liquid A,12.5 pints of liquid B, and62.5 pints of liquid C.

Was this helpful?

QuestionMix 100 pints of liquids A (10% acid), B (40% acid), and C (60% acid) for 45% acid. Find pints of each liquid.

Studdy Solution

STEP 1

Assumptions1. The total volume of the mixture is100 pints. . Liquid A contains10% acid, liquid B contains40% acid, and liquid C contains60% acid.
3. The volume of liquid A is twice the volume of liquid B.
4. The total mixture contains45% acid.

STEP 2

Let's denote the volume of liquid A as $2x$ , the volume of liquid B as $x$ , and the volume of liquid C as $y$ . We can write the equation for the total volume of the mixture as follows $2x + x + y =100$

STEP 3

The total acid in the mixture is the sum of the acid in each of the liquids. We can write the equation for the total acid in the mixture as follows $0.1(2x) +0.x +0.6y =0.45(100)$

STEP 4

implify the equationsFrom the total volume equation, we get $3x + y =100$ From the total acid equation, we get $0.2x +0.4x +0.6y =45$

STEP 5

Multiply the second equation by10 to get rid of the decimal points $2x +4x +y =450$

STEP 6

implify the equation to get $6x +6y =450$

STEP 7

Divide the entire equation by6 to simplify $x + y =75$

STEP 8

Now we have a system of two equations $3x + y =100$ $x + y =75$

STEP 9

Subtract the second equation from the first to find the value of $x$ $2x =25$

STEP 10

olve for $x$ $x =12.5$

STEP 11

Substitute $x =.5$ into the equation $x + y =75$ to find the value of $y$ $.5 + y =75$

STEP 12

olve for $y$ $y =75 -12.5 =62.5$

STEP 13

Substitute $x =12.5$ into the equation $2x = A$ to find the volume of liquid A $A =2 \times12.5 =25$ So, we need25 pints of liquid A,12.5 pints of liquid B, and62.5 pints of liquid C.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMix 100 pints of liquids A (10% acid), B (40% acid), and C (60% acid) for 45% acid. Find pints of each liquid.

Studdy Solution

STEP 1

Assumptions1. The total volume of the mixture is100 pints. . Liquid A contains10% acid, liquid B contains40% acid, and liquid C contains60% acid.3. The volume of liquid A is twice the volume of liquid B.4. The total mixture contains45% acid.

STEP 2

Let's denote the volume of liquid A as 2x2x2x, the volume of liquid B as xxx, and the volume of liquid C as yyy. We can write the equation for the total volume of the mixture as follows2x+x+y=1002x + x + y =1002x+x+y=100

STEP 3

The total acid in the mixture is the sum of the acid in each of the liquids. We can write the equation for the total acid in the mixture as follows0.1(2x)+0.x+0.6y=0.45(100)0.1(2x) +0.x +0.6y =0.45(100)0.1(2x)+0.x+0.6y=0.45(100)

STEP 4

implify the equationsFrom the total volume equation, we get3x+y=1003x + y =1003x+y=100From the total acid equation, we get0.2x+0.4x+0.6y=450.2x +0.4x +0.6y =450.2x+0.4x+0.6y=45

STEP 5

Multiply the second equation by10 to get rid of the decimal points2x+4x+y=4502x +4x +y =4502x+4x+y=450

STEP 6

implify the equation to get6x+6y=4506x +6y =4506x+6y=450

STEP 7

Divide the entire equation by6 to simplifyx+y=75x + y =75x+y=75

STEP 8

Now we have a system of two equations3x+y=1003x + y =1003x+y=100x+y=75x + y =75x+y=75

STEP 9

Subtract the second equation from the first to find the value of xxx2x=252x =252x=25

STEP 10

olve for xxxx=12.5x =12.5x=12.5

STEP 11

Substitute x=.5x =.5x=.5 into the equation x+y=75x + y =75x+y=75 to find the value of yyy.5+y=75.5 + y =75.5+y=75

STEP 12

olve for yyyy=75−12.5=62.5y =75 -12.5 =62.5y=75−12.5=62.5

STEP 13

Substitute x=12.5x =12.5x=12.5 into the equation 2x=A2x = A2x=A to find the volume of liquid AA=2×12.5=25A =2 \times12.5 =25A=2×12.5=25So, we need25 pints of liquid A,12.5 pints of liquid B, and62.5 pints of liquid C.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The total volume of the mixture is100 pints. . Liquid A contains10% acid, liquid B contains40% acid, and liquid C contains60% acid.
3. The volume of liquid A is twice the volume of liquid B.
4. The total mixture contains45% acid.

Let's denote the volume of liquid A as $2x$ , the volume of liquid B as $x$ , and the volume of liquid C as $y$ . We can write the equation for the total volume of the mixture as follows $2x + x + y =100$

The total acid in the mixture is the sum of the acid in each of the liquids. We can write the equation for the total acid in the mixture as follows $0.1(2x) +0.x +0.6y =0.45(100)$

implify the equationsFrom the total volume equation, we get $3x + y =100$ From the total acid equation, we get $0.2x +0.4x +0.6y =45$

Multiply the second equation by10 to get rid of the decimal points $2x +4x +y =450$

implify the equation to get $6x +6y =450$

Divide the entire equation by6 to simplify $x + y =75$

Now we have a system of two equations $3x + y =100$ $x + y =75$

Subtract the second equation from the first to find the value of $x$ $2x =25$

olve for $x$ $x =12.5$

Substitute $x =.5$ into the equation $x + y =75$ to find the value of $y$ $.5 + y =75$

olve for $y$ $y =75 -12.5 =62.5$

Substitute $x =12.5$ into the equation $2x = A$ to find the volume of liquid A $A =2 \times12.5 =25$ So, we need25 pints of liquid A,12.5 pints of liquid B, and62.5 pints of liquid C.