next questionjars and pencils?

Question

if i pu t 9 pencil into each jar i will have 2 jars left over if i oput 6 pencils into each jar i will have 3 pencils left over. how many pencils and jars do i have?

Answer 1

p = pencils
j = jars

9(j-2) = p
6j + 3 = p Simplify the first equation.
9j -18 = p Set left sides of the equation equal to each other since they both equal p.
6j + 3 = 9j - 18 Combine j terms on right and numeric terms on left.
21 = 3j
7 = j 7 jars.
Substitute 7 for j in an equation from above.
6*7 + 3 = p
42 + 3 = p
45 = p 45 pencils.

Check:
9 pencils in 5 jars and 2 jars left over. OK.
6 pencils in 7 jars (42) and 3 pencils left over. OK

Answer 2

let p : pencils
j : jar

9 pencils in each jar with 2 jars left over:
p/9 = j -2

6 pencils in each jar with 3 pencils left over:
(p - 3) / 6 = j

p/9 = j -2
p = 9 ( j - 2)
p = 9j - 18

(p - 3) / 6 = j
p - 3 = 6j

p = 9j - 18
p - 3 = 6j

substitute 9j - 18 for p:
9j -18 - 3 = 6j
9j - 21 = 6j
3j = 21
j = 7; 7 jars

substitute 7 for j:
p - 3 = 6 * 7
p - 3 = 42
p = 45 ; 45 pencils

45 pencils and 7 jars