Proportionality>Solving Percent Problems to Find Whole, Part, or Percent with Models(TEKS.Math.6.5.B)
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Texas 6th Grade Math › Proportionality>Solving Percent Problems to Find Whole, Part, or Percent with Models(TEKS.Math.6.5.B)
In a jar, 15% of the marbles are blue. There are 12 blue marbles. What is the total number of marbles?
80
60
72
90
Explanation
Identify part, whole, percent: part = 12, percent = 15%, whole = x. Equation method: $0.15x = 12 \Rightarrow x = 12 \div 0.15 = 80$. Proportion method: $\frac{15}{100} = \frac{12}{x}$, so $15x = 1200$ and $x = 80$. Unit-percent reasoning: if 15% is 12, then 1% is $12 \div 15 = 0.8$, so 100% is $0.8 \times 100 = 80$.
What is the missing value? 30% of 80 is ____.
30
24
26
50
Explanation
This is find the part: whole = 80, percent = 30%. Mental math: 10% of 80 is 8, so 30% is $3 \times 8 = 24$. Equation: $0.30 \times 80 = 24$. Proportion: $\frac{30}{100} = \frac{\text{part}}{80}$, so part $= \frac{30}{100} \cdot 80 = 24$.
Which equation represents this problem? "18 is what percent of 24?"
$18 = 24p$
$24 = 18p$
$\frac{18}{24} = \frac{p}{100}$
$p = \frac{24}{100}$
Explanation
Part = 18, whole = 24, percent = $p%$. The correct proportion is $\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$, so $\frac{18}{24} = \frac{p}{100}$. Equivalent equation form: $\frac{p}{100} \cdot 24 = 18$. Choice A misses dividing by 100, B reverses part and whole, and D treats $p$ as a fixed fraction unrelated to 18.
A store takes 25% off a backpack. The discount amount is 9 dollars. What was the original price of the backpack?
36
45
27
9
Explanation
This is find the whole: part (discount) = 9, percent = 25%, whole = $x$. Equation: $0.25x = 9 \Rightarrow x = 9 \div 0.25 = 36$. Proportion: $\frac{25}{100} = \frac{9}{x}$, so $25x = 900$ and $x = 36$. Check: 25% of 36 is 9.