Question

misha surveyed students in her school about what writing tool they use. she found that 75 use pens; 30 of the pen users are boys. she also found that 28 boys and 32 girls use pencils.
determine what each letter should be to complete this two - way table.

	pens	pencils	total
girls	a	32	d
total	75	b	e

a =
b =
c =
d =
e =
58
60
77
135

Explanation:

Step1: Find \(a\)

The total number of pen users is 75, and 30 of them are boys. So the number of girls who use pens (\(a\)) is \(75 - 30 = 45\).

Step2: Find \(b\)

The number of boys who use pencils is 28, and the number of girls who use pencils is 32. So the total number of pencil users (\(b\)) is \(28 + 32 = 60\).

Step3: Find \(c\)

The number of boys who use pens is 30, and the number of boys who use pencils is 28. So the total number of boys (\(c\)) is \(30 + 28 = 58\).

Step4: Find \(d\)

The number of girls who use pens is \(a = 45\), and the number of girls who use pencils is 32. So the total number of girls (\(d\)) is \(45 + 32 = 77\).

Step5: Find \(e\)

The total number of boys is \(c = 58\), and the total number of girls is \(d = 77\). So the total number of students (\(e\)) is \(58 + 77 = 135\).

Answer:

\(a = 45\), \(b = 60\), \(c = 58\), \(d = 77\), \(e = 135\)