Caden, Brandon, and Perry had a total of 103 erasers. The ratio of the number of erasers Brandon had to the number of erasers Perry had was 4:5. After Caden and Brandon gave 1/2 of their eraser, the 3 kids had 79 erasers left. How many erasers did Brandon and Perry have in the end?
How many erasers did Brandon and Perry have in the end?
Hello Guest!
c+b+p=103b:p=4:5c2+b2+p=79p=5b4c+b+5b4=103c2+b2+5b4=79
c+b+5b2=158158−b−5b2=103−b−5b455=5b2−5b455=5b4b=44Brandon has 44 erasers at the beginning.b:p=4:5p=5b4=5⋅444p=55Perry has 55 erasers at the beginning.
c=103−44−55c=4Caden has 4 erasers at the beginning.Brandon and Caden gave up half of their erasers.b−b2+p=44−442+55=77
77 erasers did Brandon and Perry have in the end.
!
C + B + P==103,
B/P ==4/5,
[C - 1/2C + B - 1/2B + P]==79, solve for B, C, P
Use substitution to get:
B==44 erasers - what Brandon started with
C ==4 erasers - what Caden started with
P ==55 erasers - what Perry started with.
44 - (44/2) ==22 erasers - Brandon had in the end.
55 - 0 ==55 erasers - what Perry had in the end.
22 + 55==77 total erasers of Brandon and Perry at the end.
4 - (4/2) ==2 erasers - what Caden had in the end.
Check: 22 + 55 + 2 ==79 total of all erasers at the end.