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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].
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