anne, ryan and joel collect empty cans for recycling. they collect a total of 1925 cans. anne collects half as many cans as ryan. joel collects twice as many cans as ryan. how many cans does joel collect?
a+r+j = 1925
2a=r
j = 2r
a = 1/2r
3 1/2r = 1925
7/2 r = 1295
r = 370
j= 370*2 = 740
A+R+J=1925
A=R/2
J=2R
R/2+R+2R=1925
3.5R=1925
R=550
J=2*550
J=1100
Let's start by assigning variables to each person's collection of cans:
Let A = number of cans Anne collects
Let R = number of cans Ryan collects
Let J = number of cans Joel collects
According to the problem, we have three pieces of information:
1. Anne collects half as many cans as Ryan: A = 0.5R
2. Joel collects twice as many cans as Ryan: J = 2R
3. The total number of cans collected by all three is 1925: A + R + J = 1925
We can use these equations to solve for the number of cans Joel collects:
Substituting A = 0.5R and J = 2R into the third equation:
0.5R + R + 2R = 1925
Combining like terms:
3.5R = 1925
Dividing both sides by 3.5:
R = 550
Substituting this value back into the equation for J:
J = 2(550) = 1100
Therefore, Joel collects 1100 cans.
To find out how many cans Joel collects, let's break down the information provided.
Let's assume that Ryan collects X cans. According to the given information, Anne collects half as many cans as Ryan, so Anne collects (1/2)X cans. Joel, on the other hand, collects twice as many cans as Ryan, so Joel collects 2X cans.
We also know that the total number of cans collected by the three of them is 1925. Therefore, we can add up their individual collections to get the equation:
X + (1/2)X + 2X = 1925
Combining like terms, we simplify the equation:
(2 + 1/2 + 1)X = 1925
(5/2)X = 1925
Now, we solve for X by multiplying both sides of the equation by 2/5:
X = (1925 * 2) / 5
X = 770
So Ryan collects 770 cans. Now, to find out how many cans Joel collects, we substitute X back into the equation:
Joel = 2X
Joel = 2 * 770
Joel = 1540
Therefore, Joel collects 1540 cans.