Problema Solution
Greg has three times as many pencils as he has erasers and five fewer rulers than pencils. He has 30 items in all. How many rulers does he have?
Answer provided by our tutors
p = number of pencils
e = number of erasers
r = number of rulers
p = 3e => p - 3e = 0
r = p - 5 => -p + r = -5
p + e + r = 30
In matrix notation:
1 -3 0 | 0
-1 0 1 | -5
1 1 1 | 30 r2 + r3 = r3
1 -3 0 | 0
-1 0 1 | -5
0 1 2 | 25 r2 + r1 = r1
0 -3 1 | -5
-1 0 1 | -5
0 1 2 | 25 -2r1 + r3 = r3
0 -3 1 | -5
-1 0 1 | -5
0 7 0 | 35
=> 7e = 35
e = 5
p = 3(5) = 15
15 + r + 5 = 30
r + 20 = 30
r = 10
Greg has 15 pencils, 5 erasers, and 10 rulers.