Math / Algebra

QuestionIt takes two scoops of detergent for every three scoops of fabric softener. If there are 28 scoops of detergent remaining, how many scoops of fabric softener will be needed? (CManeuvering the Middle LLC, 2015

Studdy Solution

STEP 1

1. The ratio of detergent to fabric softener is 2:3.
2. There are 28 scoops of detergent remaining.
3. We need to find out how many scoops of fabric softener will be needed.

STEP 2

1. Understand the ratio.
2. Define a variable for the fabric softener.
3. Set up a proportion based on the given ratio.
4. Solve the proportion to find the number of fabric softener scoops needed.

STEP 3

Understand the ratio.
The ratio of detergent to fabric softener is 2:3, meaning for every 2 scoops of detergent, there are 3 scoops of fabric softener.

STEP 4

Define a variable for the fabric softener.
Let $f$ be the number of scoops of fabric softener needed.

STEP 5

Set up a proportion based on the given ratio.
The ratio of detergent to fabric softener is 2:3, so we can write the proportion:
$\frac{2}{3} = \frac{28}{f}$

STEP 6

Solve the proportion to find the number of fabric softener scoops needed.
Cross-multiply to solve for $f$ :
$2f = 3 \times 28$
$2f = 84$

STEP 7

Divide both sides by 2 to solve for $f$ :
$f = \frac{84}{2}$
$f = 42$
The number of scoops of fabric softener needed is:
$\boxed{42}$

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QuestionIt takes two scoops of detergent for every three scoops of fabric softener. If there are 28 scoops of detergent remaining, how many scoops of fabric softener will be needed? (CManeuvering the Middle LLC, 2015

Studdy Solution

STEP 1

1. The ratio of detergent to fabric softener is 2:3.
2. There are 28 scoops of detergent remaining.
3. We need to find out how many scoops of fabric softener will be needed.

STEP 2

1. Understand the ratio.
2. Define a variable for the fabric softener.
3. Set up a proportion based on the given ratio.
4. Solve the proportion to find the number of fabric softener scoops needed.

STEP 3

Understand the ratio.
The ratio of detergent to fabric softener is 2:3, meaning for every 2 scoops of detergent, there are 3 scoops of fabric softener.

STEP 4

Define a variable for the fabric softener.
Let $f$ be the number of scoops of fabric softener needed.

STEP 5

Set up a proportion based on the given ratio.
The ratio of detergent to fabric softener is 2:3, so we can write the proportion:
$\frac{2}{3} = \frac{28}{f}$

STEP 6

Solve the proportion to find the number of fabric softener scoops needed.
Cross-multiply to solve for $f$ :
$2f = 3 \times 28$
$2f = 84$

STEP 7

Divide both sides by 2 to solve for $f$ :
$f = \frac{84}{2}$
$f = 42$
The number of scoops of fabric softener needed is:
$\boxed{42}$

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QuestionIt takes two scoops of detergent for every three scoops of fabric softener. If there are 28 scoops of detergent remaining, how many scoops of fabric softener will be needed? (CManeuvering the Middle LLC, 2015

Studdy Solution

STEP 1

1. The ratio of detergent to fabric softener is 2:3.2. There are 28 scoops of detergent remaining.3. We need to find out how many scoops of fabric softener will be needed.

STEP 2

1. Understand the ratio.2. Define a variable for the fabric softener.3. Set up a proportion based on the given ratio.4. Solve the proportion to find the number of fabric softener scoops needed.

STEP 3

Understand the ratio.The ratio of detergent to fabric softener is 2:3, meaning for every 2 scoops of detergent, there are 3 scoops of fabric softener.

STEP 4

Define a variable for the fabric softener.Let f f f be the number of scoops of fabric softener needed.

STEP 5

Set up a proportion based on the given ratio.The ratio of detergent to fabric softener is 2:3, so we can write the proportion:23=28f \frac{2}{3} = \frac{28}{f} 32​=f28​

STEP 6

Solve the proportion to find the number of fabric softener scoops needed.Cross-multiply to solve for f f f:2f=3×28 2f = 3 \times 28 2f=3×282f=84 2f = 84 2f=84

STEP 7

Divide both sides by 2 to solve for f f f:f=842 f = \frac{84}{2} f=284​f=42 f = 42 f=42The number of scoops of fabric softener needed is:42 \boxed{42} 42​

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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.

1. The ratio of detergent to fabric softener is 2:3.
2. There are 28 scoops of detergent remaining.
3. We need to find out how many scoops of fabric softener will be needed.

1. Understand the ratio.
2. Define a variable for the fabric softener.
3. Set up a proportion based on the given ratio.
4. Solve the proportion to find the number of fabric softener scoops needed.

Understand the ratio.
The ratio of detergent to fabric softener is 2:3, meaning for every 2 scoops of detergent, there are 3 scoops of fabric softener.

Define a variable for the fabric softener.
Let $f$ be the number of scoops of fabric softener needed.

Set up a proportion based on the given ratio.
The ratio of detergent to fabric softener is 2:3, so we can write the proportion:
$\frac{2}{3} = \frac{28}{f}$

Solve the proportion to find the number of fabric softener scoops needed.
Cross-multiply to solve for $f$ :
$2f = 3 \times 28$
$2f = 84$

Divide both sides by 2 to solve for $f$ :
$f = \frac{84}{2}$
$f = 42$
The number of scoops of fabric softener needed is:
$\boxed{42}$