SOLUTION: Using 7 coins to purchase an ice cream for $.85, what combination of quarters,nickles & dimes would you need equalling $.85 Use each coin at least once. I know the answer is 2

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Question 104903: Using 7 coins to purchase an ice cream for $.85, what combination of quarters,nickles & dimes would you need equalling $.85 Use each coin at least once.
I know the answer is 2 quarters, 2 dimes & 3 nickles by breaking it down to
$.25 + $.10 + $.05= $.40, leaving 4 coins to equal $.45. What is the equation for a problems 3 unknowns? And how do I go about solving without just knowing?
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
The number of coins is 7.
The total value of the coins is $0.85.
You have quarters, nickels, and dimes.
You must use at least one of each coin.
Let'assign a name to each coin.
Q-quarters
N-nickels
D-dimes
The number of coins is 7.
1.
Now let's look at the value of each coin and the total.
2.
I have to use each coin once.

We don't have enough information since we have two equations and three unknowns.
Let's see if we can go through logically and determine an answer.
Use equation 1.
1.

Substitute into equation 2.
2.
Multiply by 10 to simplify the decimals.
Substitute.

Let's solve for D in terms of Q.

3.
Let's use our inequality equations now.

From 3,

You also know from above

Now you know that

Q must take on integer values since it's a coin, then you conclude,

From 3,
3.

And finally,

2 Quarters, 2 Dimes, and 3 Nickels.
Check your answer.
2*25+2*10+3*5=85
50+20+15=85
85=85
Good answer.