QuestionDavid has 9 gallons of $20\%$ ammonia cleaner. How many gallons of $10\%$ cleaner must he add for $19\%$ ammonia?

Studdy Solution

STEP 1

Assumptions1. David has9 gallons of cleaner that is20% ammonia. David has an unlimited supply of cleaner that is10% ammonia3. David wants to obtain a batch that contains19% ammonia4. The percentage of ammonia in the final mixture is calculated as a weighted average of the percentages in the initial cleaners

STEP 2

Let's denote the amount of the10%-ammonia cleaner that David needs to add as $x$ gallons. The total amount of ammonia in the final mixture is equal to the amount of ammonia in the9 gallons of20%-ammonia cleaner plus the amount of ammonia in the $x$ gallons of10%-ammonia cleaner. This can be written as $0.20 \times9 +0.10 \times x =0.19 \times (9 + x)$

STEP 3

Now, we need to solve this equation for $x$ . First, distribute the0.19 on the right side of the equation $0.20 \times9 +0.10 \times x =0.19 \times9 +0.19 \times x$

STEP 4

Next, simplify the equation by performing the multiplications $1.8 +0.10x =1.71 +0.19x$

STEP 5

Subtract $0.10x$ from both sides of the equation to get all terms involving $x$ on one side $1.8 =1.71 +0.09x$

STEP 6

Subtract1.71 from both sides of the equation to isolate the term involving $x$ $0.09 =0.09x$

STEP 7

Finally, divide both sides of the equation by0.09 to solve for $x$ $x = \frac{0.09}{0.09} =1$ David needs to add1 gallon of the10%-ammonia cleaner to the20%-ammonia cleaner to obtain a batch that contains19% ammonia.

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QuestionDavid has 9 gallons of $20\%$ ammonia cleaner. How many gallons of $10\%$ cleaner must he add for $19\%$ ammonia?

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, we need to solve this equation for $x$ . First, distribute the0.19 on the right side of the equation $0.20 \times9 +0.10 \times x =0.19 \times9 +0.19 \times x$

STEP 4

Next, simplify the equation by performing the multiplications $1.8 +0.10x =1.71 +0.19x$

STEP 5

Subtract $0.10x$ from both sides of the equation to get all terms involving $x$ on one side $1.8 =1.71 +0.09x$

STEP 6

Subtract1.71 from both sides of the equation to isolate the term involving $x$ $0.09 =0.09x$

STEP 7

Finally, divide both sides of the equation by0.09 to solve for $x$ $x = \frac{0.09}{0.09} =1$ David needs to add1 gallon of the10%-ammonia cleaner to the20%-ammonia cleaner to obtain a batch that contains19% ammonia.

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QuestionDavid has 9 gallons of 20%20\%20% ammonia cleaner. How many gallons of 10%10\%10% cleaner must he add for 19%19\%19% ammonia?

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, we need to solve this equation for xxx. First, distribute the0.19 on the right side of the equation0.20×9+0.10×x=0.19×9+0.19×x0.20 \times9 +0.10 \times x =0.19 \times9 +0.19 \times x0.20×9+0.10×x=0.19×9+0.19×x

STEP 4

Next, simplify the equation by performing the multiplications1.8+0.10x=1.71+0.19x1.8 +0.10x =1.71 +0.19x1.8+0.10x=1.71+0.19x

STEP 5

Subtract 0.10x0.10x0.10x from both sides of the equation to get all terms involving xxx on one side1.8=1.71+0.09x1.8 =1.71 +0.09x1.8=1.71+0.09x

STEP 6

Subtract1.71 from both sides of the equation to isolate the term involving xxx0.09=0.09x0.09 =0.09x0.09=0.09x

STEP 7

Finally, divide both sides of the equation by0.09 to solve for xxxx=0.090.09=1x = \frac{0.09}{0.09} =1x=0.090.09​=1David needs to add1 gallon of the10%-ammonia cleaner to the20%-ammonia cleaner to obtain a batch that contains19% ammonia.

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QuestionDavid has 9 gallons of $20\%$ ammonia cleaner. How many gallons of $10\%$ cleaner must he add for $19\%$ ammonia?

Now, we need to solve this equation for $x$ . First, distribute the0.19 on the right side of the equation $0.20 \times9 +0.10 \times x =0.19 \times9 +0.19 \times x$

Next, simplify the equation by performing the multiplications $1.8 +0.10x =1.71 +0.19x$

Subtract $0.10x$ from both sides of the equation to get all terms involving $x$ on one side $1.8 =1.71 +0.09x$

Subtract1.71 from both sides of the equation to isolate the term involving $x$ $0.09 =0.09x$

Finally, divide both sides of the equation by0.09 to solve for $x$ $x = \frac{0.09}{0.09} =1$ David needs to add1 gallon of the10%-ammonia cleaner to the20%-ammonia cleaner to obtain a batch that contains19% ammonia.