Question

objective 4 - contrast part - to - part and part - to - whole ratios
guided practice activity #5 - student expenses
use the following data for public two - year in - district student expenses for 2017 - 18 to answer the questions.
tuition and fees room and board books and supplies transportation other expenses total
$3,570 $8,400 $1,420 $1,780 $2,410 $17,580
a b 100
c 1

1. compute the part - to - whole ratio of tuition and fees to total expenses with the second quantity scaled to 100. use the ratio in a sentence.
2. compute the part - to - part ratio of tuition and fees to books and supplies. use the ratio in a sentence.

Explanation:

Step1: Calculate part - to - whole ratio for tuition and fees to total expenses

Let the part (tuition and fees) be $a = 3570$ and the whole (total expenses) be $b=17580$. The ratio is $\frac{a}{b}=\frac{3570}{17580}$.
To scale the second quantity to 100, we set up the proportion $\frac{3570}{17580}=\frac{x}{100}$. Cross - multiplying gives $17580x = 3570\times100$, so $x=\frac{3570\times100}{17580}\approx20.3$.

Step2: Calculate part - to - part ratio for tuition and fees to books and supplies

Let the first part (tuition and fees) be $m = 3570$ and the second part (books and supplies) be $n = 1420$. The ratio is $\frac{m}{n}=\frac{3570}{1420}=\frac{357}{142}\approx2.51$.

Answer:

1. The part - to - whole ratio of tuition and fees to total expenses with the second quantity scaled to 100 is approximately 20.3:100. This means that tuition and fees make up about 20.3% of the total student expenses.
2. The part - to - part ratio of tuition and fees to books and supplies is approximately 2.51:1. This means that for every dollar spent on books and supplies, about 2.51 dollars are spent on tuition and fees.