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If Hugo has 4 times as many quarters as nickels and they have a combined value of 840 cents, how many of each coin does he have?

2 Answers

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Let Q be the number of quarters and N be the number of nickels that Hugo has. We are given that Hugo has 4 * N quarters and that the total number of quarters and nickels is worth 840 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, the total number of quarters is worth 25 * Q cents and the total number of nickels is worth 5 * N cents. Therefore, the total number of quarters and nickels is worth 25 * Q + 5 * N cents. Since the total number of quarters and nickels is worth 840 cents, we can set up the following equation to represent this information:

25 * Q + 5 * N = 840

We are also given that Hugo has 4 * N quarters, so we can set up the following equation to represent this information:

Q = 4 * N

We can solve this system of equations to find the number of quarters and nickels that Hugo has. Substituting the value of Q in the second equation into the first equation, we get the following:

25 * (4 * N) + 5 * N = 840

Distributing the 25 on the left side of the equation, we get the following:

100 * N + 5 * N = 840

Combining like terms, we get the following:

105 * N = 840

Dividing both sides of the equation by 105, we get the following:

N = 8

Substituting the value of N into the second equation, we get the following:

Q = 4 * 8

Solving for Q, we get the following:

Q = 32

Therefore, Hugo has 8 nickels and 32 quarters.

User BinaryDi
by
9.3k points
3 votes

Answer:

32 quarters

8 nickels

Explanation:

Information:

  • 1 quarter = 25 cents
  • 1 nickel = 5 cents

Define the variables:

  • Let x be the number of quarters.
  • Let y be the number of nickels.

If Hugo has 4 times as many quarters as nickels:


\implies x=4y

If the combined value of quarters and nickels is 840 cents:


\implies 25x+5y=840

Substitute the first equation into the second equation and solve for y:


\implies 25(4y)+5y=840


\implies100y+5y=840


\implies 105y=840


\implies y=8

Substitute the found value of y into the first equation and solve for x:


\implies x=4(8)


\implies x=32

Therefore, Hugo has:

  • 32 quarters
  • 8 nickels
User DuckPyjamas
by
8.9k points

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