Red, Green Beans and Bottles

Algebra Level 2

I have some red, green beans and bottles. If I put 5 5 beans into each bottle, nothing will be left. Instead, if I put 3 3 red beans into each bottle, I will have 1 1 red bean left. However, if I put 3 3 green beans into each bottle, I will have 2 2 green beans and 2 2 bottles left.

Express red beans as x x , green beans as y y , bottles as z z , find the value of x y z − x y xyz-xy


The answer is 100.

Wenn Chuaan Lim by Wenn Chuaan Lim , 33, Malaysia

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1 solution

Wenn Chuaan Lim
Jun 5, 2014

Express red beans as x x , green beans as y y , bottles as z z .
1. x + y 5 = z \frac{x+y}{5}=z
x + y = 5 z x+y=5z
2. x − 1 3 = z \frac{x-1}{3}=z
x = 3 z + 1 x=3z+1
3. y − 2 3 = z − 2 \frac{y-2}{3}=z-2
y = 3 z − 4 y=3z-4
Substitute x x and y y into the first equation, and you will get z = 3 z=3 .
Next, substitute z z into the second and third equations, the solution will be x = 10 x=10 and y = 5 y=5 .
Finally, solve the algebraic expressions x y z − x y xyz-xy which is
( 10 ) ( 5 ) ( 3 ) − ( 10 ) ( 5 ) (10)(5)(3)-(10)(5)
= 150 − 50 150-50
= 100 100


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