"Ten thieves stole into Abdul's shop. Some of them were armed and some were unarmed. The armed ones were those of senior rank. Anyway, they stole a bag of fifty-six pearls. When it came to dividing them up, each senior robber took six pearls, and each junior robber got five. How many of the robbers were senior?"
SHOW WORK PLEASE.
2006-10-10 09:57:04 · 3 answers · asked by yankee_914 1 in Science & Mathematics ➔ Mathematics
Let x = senior robbers, and y = junior robbers
We know that x + y = 10, there are 10 robbers
We know that 6x +5y = 56, since each senior roober got 6 pearls, each junior obber got 5 and there were 56 total.
Using the x+y=10 formula, we solve it for y:
y = 10 - x
Substituting this into the other equation gives:
6x +5(10 - x) = 56
Now solve for x:
6x + 50 - 5x = 56
x = 6
There were 6 senior robbers and 4 junior robbers.
That would be 36 pearls for the senior robbers and 20 for the junior robbers for a toal of 56.
Check!
2006-10-10 10:04:15 · answer #1 · answered by Anonymous · 0⤊ 0⤋
6 senior robbers = 6*6 = 36pearls
4 junior robbers = 5*4 = 20pearls
Total 56 pearls
2006-10-10 10:05:24 · answer #2 · answered by syam p 2 · 0⤊ 0⤋
Let x be the number of senior robbers, y the junior.
Then x+y=10, because there are 10 robbers, and 6x+5y=56, because there were 56 pearls, with each senior getting 6 and each junior getting 5.
To solve the system of equations
x+y=10
6x+5y=56
Multipy the first equation by 6:
6x+6y=60
6x+5y=56
Subtract the second equation from the first:
y=4
So since x+y=10, x=6.
2006-10-10 10:01:24 · answer #3 · answered by James L 5 · 1⤊ 0⤋