Trip has 15 coins worth 95 cents.Four of the coins are each worth twice as much as the rest.Construct a math argument to justify the conjecture that Trip has 11 nickles and 4 dimes.

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05-02-2018
Mathematics

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Trip has 15 coins worth 95 cents.Four of the coins are each worth twice as much as the rest.Construct a math argument to justify the conjecture that Trip has 11 nickles and 4 dimes.

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Dibny Dibny · Answer 1 · 2018-02-13T08:28:03+01:00

Let's assign x to the value of one coin. Since four coins are twice the value of x, we'll have the term [tex]4(2x)[/tex] or [tex]8x[/tex] for these coins. The rest of the eleven coins have the value of x thus we'll have [tex]11x[/tex] as one of the terms, too.

If we add these two terms, we should get a sum of $0.95 since that's the total worth of Trip's coins. We can then solve for x to find how much each of the 11 coins of Trip are worth.

[tex]8x+11x=0.95[/tex]
[tex]19x=0.95[/tex]
[tex]x=0.05[/tex]

Since 11 coins of Trip are worth $0.05 each, we have successfully verified that Trip has 11 nickles. Furthermore, the 4 remaining coins would automatically be dimes since it's twice the value of nickel.