Question 1194331: Need help setting up the equations.
A treasure chest contains 70 gold coins, 50 silver coins, and 100 bronze coins. How many additional gold coins must be added to the 220 coins already in the treasure chest so that half of the coins in the treasure chest are gold?
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A treasure chest contains 70 gold coins, 50 silver coins, and 100 bronze coins.
How many additional gold coins must be added to the 220 coins already in the treasure chest so that half of the coins in the treasure chest are gold?
:
let g = no. of gold coins that have to be added
g + 70 = .5(g + 220)
g + 70 = .5g + 110
g - .5g = 110 - 70
.5g = 40
g = 80 gold coins to be added
:
Check:
80 + 220 = 300
70 + 80 = 150, half of the total
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
Need help setting up the equations.
A treasure chest contains 70 gold coins, 50 silver coins, and 100 bronze coins.
How many additional gold coins must be added to the 220 coins already in the treasure chest
so that half of the coins in the treasure chest are gold?
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The solution by the other tutor in nice, is correct and satisfies the problem's request.
But the problem can be easy solved mentally, as I show it below.
Originally, there are 70 gold coins and 50+100 = 150 not-gold coins in the treasure.
We want to add gold coins to the treasure in a way to have half of the coins in the treasure chest as a gold coins.
Obviously, the goal will be achieved, when the new total gold coins will be 150.
For it, 150-70 = 80 gold coins must be added. ANSWER
Solved.
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In this way, the problem can be easily solved by a 3-rd grade student,
who ever never heard about solving Math problems using equations.
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