Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Sure, let's solve these percent problems step-by-step using more than one strategy.
Part (a):
### Problem:
[tex]\( 48 \)[/tex] is [tex]\( x \% \)[/tex] of [tex]\( 80 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{48}{80} = \frac{x}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[ 48 \times 100 = 80x \][/tex]
[tex]\[ 4800 = 80x \][/tex]
3. Divide both sides by 80:
[tex]\[ x = \frac{4800}{80} \][/tex]
4. Perform the division:
[tex]\[ x = 60 \][/tex]
So, [tex]\( 48 \)[/tex] is [tex]\( 60\% \)[/tex] of [tex]\( 80 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{48}{80} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 0.6 \times 100 = 60 \][/tex]
So again, [tex]\( 48 \)[/tex] is [tex]\( 60\% \)[/tex] of [tex]\( 80 \)[/tex].
Part (b):
### Problem:
[tex]\( 230 \)[/tex] is [tex]\( y \% \)[/tex] of [tex]\( 200 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{230}{200} = \frac{y}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( y \)[/tex]:
[tex]\[ 230 \times 100 = 200y \][/tex]
[tex]\[ 23000 = 200y \][/tex]
3. Divide both sides by 200:
[tex]\[ y = \frac{23000}{200} \][/tex]
4. Perform the division:
[tex]\[ y = 115 \][/tex]
So, [tex]\( 230 \)[/tex] is [tex]\( 115\% \)[/tex] of [tex]\( 200 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{230}{200} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 1.15 \times 100 = 115 \][/tex]
So again, [tex]\( 230 \)[/tex] is [tex]\( 115\% \)[/tex] of [tex]\( 200 \)[/tex].
Part (c):
### Problem:
[tex]\( 270 \)[/tex] is [tex]\( z \% \)[/tex] of [tex]\( 900 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{270}{900} = \frac{z}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( z \)[/tex]:
[tex]\[ 270 \times 100 = 900z \][/tex]
[tex]\[ 27000 = 900z \][/tex]
3. Divide both sides by 900:
[tex]\[ z = \frac{27000}{900} \][/tex]
4. Perform the division:
[tex]\[ z = 30 \][/tex]
So, [tex]\( 270 \)[/tex] is [tex]\( 30\% \)[/tex] of [tex]\( 900 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{270}{900} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 0.3 \times 100 = 30 \][/tex]
So again, [tex]\( 270 \)[/tex] is [tex]\( 30\% \)[/tex] of [tex]\( 900 \)[/tex].
Part (a):
### Problem:
[tex]\( 48 \)[/tex] is [tex]\( x \% \)[/tex] of [tex]\( 80 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{48}{80} = \frac{x}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[ 48 \times 100 = 80x \][/tex]
[tex]\[ 4800 = 80x \][/tex]
3. Divide both sides by 80:
[tex]\[ x = \frac{4800}{80} \][/tex]
4. Perform the division:
[tex]\[ x = 60 \][/tex]
So, [tex]\( 48 \)[/tex] is [tex]\( 60\% \)[/tex] of [tex]\( 80 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{48}{80} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 0.6 \times 100 = 60 \][/tex]
So again, [tex]\( 48 \)[/tex] is [tex]\( 60\% \)[/tex] of [tex]\( 80 \)[/tex].
Part (b):
### Problem:
[tex]\( 230 \)[/tex] is [tex]\( y \% \)[/tex] of [tex]\( 200 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{230}{200} = \frac{y}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( y \)[/tex]:
[tex]\[ 230 \times 100 = 200y \][/tex]
[tex]\[ 23000 = 200y \][/tex]
3. Divide both sides by 200:
[tex]\[ y = \frac{23000}{200} \][/tex]
4. Perform the division:
[tex]\[ y = 115 \][/tex]
So, [tex]\( 230 \)[/tex] is [tex]\( 115\% \)[/tex] of [tex]\( 200 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{230}{200} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 1.15 \times 100 = 115 \][/tex]
So again, [tex]\( 230 \)[/tex] is [tex]\( 115\% \)[/tex] of [tex]\( 200 \)[/tex].
Part (c):
### Problem:
[tex]\( 270 \)[/tex] is [tex]\( z \% \)[/tex] of [tex]\( 900 \)[/tex].
#### Strategy 1: Proportion Method
1. Set up the proportion:
[tex]\[ \frac{270}{900} = \frac{z}{100} \][/tex]
2. Cross-multiply to solve for [tex]\( z \)[/tex]:
[tex]\[ 270 \times 100 = 900z \][/tex]
[tex]\[ 27000 = 900z \][/tex]
3. Divide both sides by 900:
[tex]\[ z = \frac{27000}{900} \][/tex]
4. Perform the division:
[tex]\[ z = 30 \][/tex]
So, [tex]\( 270 \)[/tex] is [tex]\( 30\% \)[/tex] of [tex]\( 900 \)[/tex].
#### Strategy 2: Percent Equation
1. Use the percent equation [tex]\( \frac{\text{Part}}{\text{Whole}} \times 100 = \%\)[/tex]:
[tex]\[ \frac{270}{900} \times 100 = \% \][/tex]
2. Perform the division:
[tex]\[ 0.3 \times 100 = 30 \][/tex]
So again, [tex]\( 270 \)[/tex] is [tex]\( 30\% \)[/tex] of [tex]\( 900 \)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
