SOLUTION: Taylor collected 3 times as many pebbles as Marco. Gina collected 21 fewer pebbles than Taylor. They collected 427 pebbles altogether. How many pebbles did Gina collect?
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Question 807325: Taylor collected 3 times as many pebbles as Marco. Gina collected 21 fewer pebbles than Taylor. They collected 427 pebbles altogether. How many pebbles did Gina collect?
I am a parent and need to be able to show my 6th grader how to solve this problem; not just an answer, please.
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
First assign a variable for the no. of pebbles each had
t = Taylor's pebbles
m = Marco's
g = Gino's
:
Write an equation for each statement.
Taylor collected 3 times as many pebbles as Marco.
t = 3m
Gina collected 21 fewer pebbles than Taylor.
g = t - 21
They collected 427 pebbles altogether.
t + m + g = 147
:
How many pebbles did Gina collect?
We want to get varibles g and m in terms of t, then we have only one variable to deal with.
g = (t-21) so that one is OK,
however
3m = t
divide both sides by 3
m = t/3
:
In the last equation, replace g with (t-21) and m with t/3
t + (t-21) + t/3 = 147
Get rid of the fraction, multiply by 3 and you have
3t + 3(t-21) + t = 3(147)
3t + 3t - 63 + t = 441
7t = 441 + 63
7t = 504
t = 504/7
t = 72 pebbles for Taylor
then
m = 72/3
m = 24 pebbles for Marco
and
g = 72 - 21
g = 51 pebbles for Gina
:
The last step is to check and see if:
72 + 24 + 51 = 147
:
:
This is a common method in solving these multi-variable equations, you can
see that it is pretty logical, if you follow each step. CK
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Taylor collected 3 times as many pebbles as Marco. Gina collected 21 fewer pebbles than Taylor. They collected 427 pebbles altogether. How many pebbles did Gina collect?
Amount of pebbles collected by Gina:
You can do the check!!
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