Question 227110: There are 80 bins that hold 1600 tons. Some bin hold 20 tons and some hold 25 tons. how many of each bin is needed to hold 1600 tons? Found 2 solutions by drj, Theo:Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! There are 80 bins that hold 1600 tons. Some bin hold 20 tons and some hold 25 tons. how many of each bin is needed to hold 1600 tons?
Step 1. Let x be the number of 20 ton bins
Step 2. Let 80-x be the number of 25 ton bins since there are a total of 80 bins.
Step 3. Let 20x be the amount held by 20-ton bins
Step 4. Let 25(80-x) be the amount held by 25-ton bins
Step 5. Then be the total amount. Or . Simplifying yields:
Step 6. Solving yields the following steps
Add 5x-1600 to both sides of the equation
Divide by 5 to bth sides of the equation
and
Step 7. ANSWER: There are 80 20-ton bins and 0 25-ton bins to hold a total of 1600 tons.
I hope the above steps were helpful.
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And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
If you didn't know that, you would solve this puzzle as follows:
Let x = number of bins holding 20 tons.
Let y = number of bins holding 25 tons.
Total number of bins is 80 so x + y = 80 is one of your equations.
Total tons required to be held is 1600 tons, so 20*x + 25*y = 1600
You would solve both these equations simultaneously.
this means that the same value for x and y would solve both equations at the same time.
Your two equations are:
x + y = 80
20x + 25y = 1600
You can solve by substitution or you can solve by elimination.
We'll do elimination.
You want one of the variables to drop out of the two equations so you are left with one equation and one variable.
You do this by making the same variable in each equation have same coefficient.
You can then add or subtract the two equations to eliminate that variable and be left with one equation with one unknown.
Here's how we do it.
Your equations are again.
x + y = 80
20x + 25y = 1600
Multiply both sides of the first equation by 25. This allows the coefficient of y in the first equation to be the same as the coefficdient of y in the second equation and it doesn't change the equality because you are doing the same thing on both sides of the equal sign.
You get:
25x + 25y = 2000
20x + 25y = 1600
Subtract the second equation from the first equation to get:
5x = 400
Divide both sides of this equation by 5 to get:
x = 80
Use the value of x to solve for y in one of your equations.
Use x + y = 80.
You get:
y = 0
You have:
x = 80
y = 0
Replace x and y in both original equations to see if this solves both equations.
First equation is x + y = 80 and x = 80 and y = 0 works ok.
Second equation is 20x+ 25y = 1600 and x = 80 and y = 0 works ok because 20*80 = 1600.
Your answer is 80 bins of 20 tons will handle 1600 tons.
Your assumption in the equality equation of x + y = 80 was that all bins had to be used.
That's why your answer used all 80 bins.
Suppose you only wanted to use 70 bins.
Your equation of total number of bins used would have been x + y = 70
that changes the equation.
The two simultaneous equations would have been.
x + y = 70
20x + 25y = 1600
You can also solve this by substitution.
Solve for x in the first equation to get x = 70 - y
Substitute for x in the second equation to get:
20*(70-y) + 25y = 1600
remove partntheses to get:
1400 - 20y + 25y = 1600
subtract 1400 from both sides simplify and combine both sides to get:
5y = 200
divide both sides by 5 to get:
y = 40
Since x + y = 70, then x = 30
30 * 20 + 40 * 25 = 600 + 1000 = 1600
The answer to your problem, however, was 80 bins because that's the number that you wanted to use.
