School scores

Dorothy had a total of 22 grades in her school book. She had one-third as many grade 1s as grade 3s. She had only two grade 2s. How many grade 1s and grade 3s did Dorothy have in her school book?

Final Answer:

a =  5
b =  15

Step-by-step explanation:

a+b = 22-2
a=b/3

a+b = 20
3a-b = 0

Pivot: Row 1 ↔ Row 2
3a-b = 0
a+b = 20

Row 2 - 1/3 · Row 1 → Row 2
3a-b = 0
1.33b = 20


b = 20/1.33333333 = 15
a = 0+b/3 = 0+15/3 = 5

a = 5
b = 15

Our linear equations calculator calculates it.

Try another example