# Achef uses 4 3/4 cups of broth for 10 servings of soup. how much broth used in each serving of soup? let x represent the

###### Question:

## Answers

0.475 cups of broth per serving.

Explanation:

1) Ratio given:

i) To facilitate the operations, transform the mixed number 4 3/4 cups into improper fraction:

4 + 3/4 = [16 + 3] / 4 = 19 / 4

ii) ratio broth: servings

[tex]\frac{ \frac{19}{4}cups }{10servings}[/tex]

2) Proportion with the unknown number of cups of broth per serving:

[tex]\frac{ \frac{19}{4}cups }{10servings}= \frac{x}{1serving}[/tex]

3) Solve for the unknown:

x = [19 / 4] cups × 1 serving / 10 servings = 19 / 40 cups = 0.475 cups

In one serving is used 19/40 cups

4 3/4= 19/4

19/4 :10=19/4:10/1

19/4x1/10=19/40

check:

19/4=4.75 4.45/10=0.474

19/40=0.475

oof well I don't know what this is just needed some point but someone will help you don't worry

Convert 4 and 3/4 into an improper fraction: 19/4. Then, divide 19/4 into 10, but to divide fractions, you multiply by the reciprocal. So: 19/4•1/10=19/40. So the chef uses 19/40 cup of broth in each serving.

Let's firstly convert the mixed fraction to "improper" and then proceed,

[tex]\bf \begin{array}{ccll} \stackrel{broth}{cups}&servings\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4\frac{3}{4}&10\\\\ x&1 \end{array}\implies \cfrac{\quad \stackrel{mixed}{4\frac{3}{4}}\quad }{x}=\cfrac{10}{1}\implies \cfrac{\quad \frac{4\cdot 4+3}{4}\quad }{x}=\cfrac{10}{1}[/tex]

[tex]\bf \cfrac{\quad \stackrel{improper}{\frac{19}{4}}\quad }{x}=\cfrac{10}{1}\implies \cfrac{\quad \frac{19}{4}\quad }{\frac{x}{1}}=\cfrac{10}{1}\implies \cfrac{19}{4}\cdot \cfrac{1}{x}=\cfrac{10}{1}\implies \cfrac{19}{4x}=\cfrac{10}{1} \\\\\\ 19=40x\implies \cfrac{19}{40}=x[/tex]

Set up a proportion. 4 3/4 cup broth is to 10 servings as x cups broth is to 1 serving soup.

x= amount of broth in one serving

(4 3/4)/10= x/1

cross multiply

(4 3/4)(1)= 10x

convert 4 3/4 to improper fraction

(19/4)(1)= 10x

19/4= 10x

divide both sides by 10

19/4 ÷ 10= x

to divide fractions, multiply by reciprocal of 10

19/4 * 1/10= x

multiply numerators; multiply denominators

(19*1)/(4*10)= x

19/40 cup= x

ANSWER: 19/40 cup in one serving

Hope this helps! :)

Your proportion is correct.

Cross multiply.

10x = 4 3/4

10x = 19/4

x = 19/40

You need 19/40 of a cup.