Percent of an Amount – Word Problems 3

Question 1 of 4

A baker puts in

75 g

$75 \text(g)$ of cocoa,

150 g

$150 \text(g)$ of sugar,

225 g

$225 \text(g)$ of flour and

50 g

$50 \text(g)$ of butter for her chocolate mud cake. Find the percentages of each ingredient.

$Cocoa$ $\text(Cocoa)$ = (15) $%$ $%$

$Sugar$ $\text(Sugar)$ = (30) $%$ $%$

$Flour$ $\text(Flour)$ = (45) $%$ $%$

$Butter$ $\text(Butter)$ = (10) $%$ $%$

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First, list down the known values for each ingredient.

Cocoa = 75 g

$\text(Cocoa)=75 \text(g)$

Sugar = 150 g

$\text(Sugar)=150 \text(g)$

Flour = 225 g

$\text(Flour)=225 \text(g)$

Butter = 50 g

$\text(Butter)=50 \text(g)$

Next, get the total amount of ingredients by adding the value of all the ingredients.

$Total Amount$ $\text(Total Amount)$	$=$ $=$	$75$ $75$ $+$ $+$ $150$ $150$ $+$ $+$ $225$ $225$ $+$ $+$ $50$ $50$
	$=$ $=$	$500$ $500$

Then, solve for the percentage of each amount by multiplying the fraction of the ingredients by

100 %

$100%$ .

Cocoa

$\text(Cocoa)$

	$\frac{\color{#9a00c7}{75}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{75}{500} \times \frac{100}{1}$ $75/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{75}{5} \times \frac{1}{1}$ $75/5times1/1$	Simplify

$=$ $=$	$\frac{75}{5}$

$=$ $=$	$15 %$ $15%$

Sugar

$\text(Sugar)$

	$\frac{\color{#00880A}{150}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{150}{500} \times \frac{100}{1}$ $150/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{150}{5} \times \frac{1}{1}$ $150/5times1/1$	Simplify

$=$ $=$	$\frac{150}{5}$

$=$ $=$	$30 %$ $30%$

Flour

$\text(Flour)$

	$\frac{\color{#e85e00}{225}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{225}{500} \times \frac{100}{1}$ $225/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{225}{5} \times \frac{1}{1}$ $225/5times1/1$	Simplify

$=$ $=$	$\frac{225}{5}$

$=$ $=$	$45 %$ $45%$

Butter

$\text(Butter)$

	$\frac{\color{#007DDC}{50}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{50}{500} \times \frac{100}{1}$ $50/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{50}{5} \times \frac{1}{1}$ $50/5times1/1$	Simplify

$=$ $=$	$\frac{50}{5}$

$=$ $=$	$10 %$ $10%$

Cocoa = 15 %

$\text(Cocoa)=15%$

Sugar = 30 %

$\text(Sugar)=30%$

Flour = 45 %

$\text(Flour)=45%$

Butter = 10 %

$\text(Butter)=10%$

Question 2 of 4

A tub of ice cream contains

150 g

$150 \text(g)$ of milk solids,

135 g

$135 \text(g)$ of cream,

125 g

$125 \text(g)$ of sugar and

90 g

$90 \text(g)$ of butter. Find the percentages of each ingredient.

$Milk Solids$ $\text(Milk Solids)$ = (30) $%$ $%$

$Cream$ $\text(Cream)$ = (27) $%$ $%$

$Sugar$ $\text(Sugar)$ = (25) $%$ $%$

$Butter$ $\text(Butter)$ = (18) $%$ $%$

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First, list down the known values for each ingredient.

Milk Solids = 150 g

$\text(Milk Solids)=150 \text(g)$

Cream = 135 g

$\text(Cream)=135 \text(g)$

Sugar = 125 g

$\text(Sugar)=125 \text(g)$

Butter = 90 g

$\text(Butter)=90 \text(g)$

Next, get the total amount of ingredients by adding the value of all the ingredients.

$Total Amount$ $\text(Total Amount)$	$=$ $=$	$150$ $150$ $+$ $+$ $135$ $135$ $+$ $+$ $125$ $125$ $+$ $+$ $90$ $90$
	$=$ $=$	$500$ $500$

Then, solve for the percentage of each amount by multiplying the fraction of the ingredients by

100 %

$100%$ .

Milk Solids

$\text(Milk Solids)$

	$\frac{\color{#9a00c7}{150}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{150}{500} \times \frac{100}{1}$ $150/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{150}{5} \times \frac{1}{1}$ $150/5times1/1$	Simplify

$=$ $=$	$\frac{150}{5}$

$=$ $=$	$30 %$ $30%$

Cream

$\text(Cream)$

	$\frac{\color{#00880A}{135}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{135}{500} \times \frac{100}{1}$ $135/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{135}{5} \times \frac{1}{1}$ $135/5times1/1$	Simplify

$=$ $=$	$\frac{135}{5}$

$=$ $=$	$27 %$ $27%$

Sugar

$\text(Sugar)$

	$\frac{\color{#e85e00}{125}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{125}{500} \times \frac{100}{1}$ $125/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{125}{5} \times \frac{1}{1}$ $125/5times1/1$	Simplify

$=$ $=$	$\frac{125}{5}$

$=$ $=$	$25 %$ $25%$

Butter

$\text(Butter)$

	$\frac{\color{#007DDC}{90}}{\color{#A57200}{500}}\times100\%$

$=$ $=$	$\frac{90}{500} \times \frac{100}{1}$ $90/500times100/1$	Convert values to fraction form

$=$ $=$	$\frac{90}{5} \times \frac{1}{1}$ $90/5times1/1$	Simplify

$=$ $=$	$\frac{90}{5}$

$=$ $=$	$18 %$ $18%$

Milk Solids = 30 %

$\text(Milk Solids)=30%$

Cream = 27 %

$\text(Cream)=27%$

Sugar = 25 %

$\text(Sugar)=25%$

Butter = 18 %

$\text(Butter)=18%$

Question 3 of 4

A bakery sells

300

$300$ loaves of bread every day. If

15 %

$15%$ of the bread they sell is gluten-free, how many loaves are not gluten-free?

(255) $loaves of bread$ $\text(loaves of bread)$

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First, summarise the data and draw a diagram for easier understanding of the problem

Total loaves of bread sold = 300

$\text(Total loaves of bread sold)=300$

Percentage of gluten-free loaves = 15 %

$\text(Percentage of gluten-free loaves)=15%$

Percentage of total loaves sold = 100 %

$\text(Percentage of total loaves sold)=100%$

Percentage of not gluten-free loaves = ?

$\text(Percentage of not gluten-free loaves)=?$

Next, find the percentage of loaves that are not gluten-free.

Do this by subtracting the percentage of gluten-free loaves $(15 %)$ $(15%)$ from $100 %$ $100%$

$% of not gluten-free loaves$ $% \text(of not gluten-free loaves)$	$=$ $=$	$100$ $100$ $-$ $-$ $15$ $15$
	$=$ $=$	$85 %$ $85%$

$85 %$ $85%$ of the loaves are not gluten-free.

Finally, multiply the percentage to the total number of loaves which is $300$ $300$

$Not Gluten-Free Loaves$ $\text(Not Gluten-Free Loaves)$	$=$ $=$	$85 %$ $85%$ $\times$ $times$ $300$ $300$

	$=$ $=$	$\frac{85}{100} \times \frac{300}{1}$ $85/100xx300/1$	Convert values to fraction form

	$=$ $=$	$\frac{85}{1} \times \frac{3}{1}$ $85/1xx3/1$	Cancel the zeros

	$=$ $=$	$\frac{85\times3}{1}$

	$=$ $=$	$\frac{255}{1}$ $255/1$

	$=$ $=$	$255$ $255$

Hence, $\underline{255\;\text{loaves of bread}}$ are not gluten-free.

255 loaves of bread

$255 \text(loaves of bread)$

Question 4 of 4

In a town with

410

$410$ homes,

80 %

$80%$ of the homes were affected by a blackout. How many homes were not affected?

(82) $homes$ $\text(homes)$

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First, summarise the data and draw a diagram for easier understanding of the problem

Total number of homes = 410

$\text(Total number of homes)=410$

Percentage of homes affected = 80 %

$\text(Percentage of homes affected)=80%$

Percentage of total homes = 100 %

$\text(Percentage of total homes)=100%$

Percentage of homes not affected = ?

$\text(Percentage of homes not affected)=?$

Next, find the percentage of homes that are not affected by the blackout.

Do this by subtracting the percentage of affected homes $(80 %)$ $(80%)$ from $100 %$ $100%$

$% of homes not affected$ $% \text(of homes not affected)$	$=$ $=$	$100$ $100$ $-$ $-$ $80$ $80$
	$=$ $=$	$20 %$ $20%$

$20 %$ $20%$ of the homes are not affected.

Finally, multiply the percentage by the total number of homes which is $410$ $410$

$Homes not affected$ $\text(Homes not affected)$	$=$ $=$	$20 %$ $20%$ $\times$ $times$ $410$ $410$

	$=$ $=$	$\frac{20}{100} \times \frac{410}{1}$ $20/100times410/1$	Convert values to fraction form

	$=$ $=$	$\frac{2}{1} \times \frac{41}{1}$ $2/1times41/1$	Simplify

	$=$ $=$	$\frac{2\times41}{1}$

	$=$ $=$	$82$ $82$

Hence, $\underline{82\;\text{homes}}$ were not affected by the blackout.

82 homes

$82 \text(homes)$

Percent of an Amount – Word Problems 3

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