Mr. Richards' class is holding a canned food drive for charity. Juliet collected 10 more cans than Rosana. Santiago collected twice as many cans as Juliet. If they collect collected 130 together, any cans did Juliet collect?

Question

Mr. Richards' class is holding a canned food drive for charity. Juliet collected 10 more cans than Rosana.  Santiago collected twice as many cans as Juliet. If they collect collected 130 together, any cans did Juliet collect?

Eva Adamson · Accepted Answer

See a solution process below:

First, let's name our variables: We are told the three students collected #130# cans so we can write: #j + r + s = 130# We also know: #j = r + 10# because Juliet collect #10# more cans than Rosana. We also know: #s = 2j# because Santiago collected two as many cans as Juliet We can substitute #r + 10# which is equal to #j# into this equation to give: #s = 2(r + 10)# #s = (2 * r) + (2 * 10)# #s = 2r + 20# In the original equation we can now substitute #r + 10# for #j# and we can substitute #2r + 20# for #s# and solve for #r#: #j + r + s = 130# becomes: #r + 10 + r + 2r + 20 = 130# #r + r + 2r + 10 + 20 = 130# #1r + 1r + 2r + 10 + 20 = 130# #(1 + 1 + 2)r + (10 + 20) = 130# #4r + 30 = 130# #4r + 30 - color(red)(30) = 130 - color(red)(30)# #4r + 0 = 100# #4r = 100# #(4r)/color(red)(4) = 100/color(red)(4)# #(color(red)(cancel(color(black)(4)))r)/cancel(color(red)(4)) = 25# #r = 25# Rosana: Rosana collected 25 cans. Santiago: We an substitute #25# for #r# in Santiago's equation: #s = 2r + 20# becomes: #s = (2 * 25) + 20# #s = 50 + 20# #s = 70# Santiago collected 70 cans Juliet: We an substitute #25# for #r# in Juliet's equation: #j = r + 10# becomes: #j = 25 + 10# #j = 35# Juliet collected 35 cans. Total Cans Collected: 35 + 25 + 70 = 60 + 70 = 130#

Nathan Axel · Answer

undefined Let's denote the number of cans Rosana collected as $ R $, Juliet as $ J $, and Santiago as $ S $. We are given that Juliet collected 10 more cans than Rosana ($ J = R + 10 $) and Santiago collected twice as many cans as Juliet ($ S = 2J $). We also know that together they collected 130 cans ($ R + J + S = 130 $).

Substitute the expressions for $ J $ and $ S $ in terms of $ R $ into the equation $ R + J + S = 130 $:

$$ R + (R + 10) + 2(R + 10) = 130 $$

Now, solve for $ R $:

$$ R + R + 10 + 2R + 20 = 130 $$
$$ 4R + 30 = 130 $$
$$ 4R = 100 $$
$$ R = 25 $$

So, Rosana collected 25 cans. Since Juliet collected 10 more than Rosana, Juliet collected $ J = R + 10 = 25 + 10 = 35 $ cans. Therefore, Juliet collected 35 cans.