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.
Answer:
32 quarters
8 nickels
Step-by-step explanation:
Information:
Define the variables:
If Hugo has 4 times as many quarters as nickels:
[tex]\implies x=4y[/tex]
If the combined value of quarters and nickels is 840 cents:
[tex]\implies 25x+5y=840[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 25(4y)+5y=840[/tex]
[tex]\implies100y+5y=840[/tex]
[tex]\implies 105y=840[/tex]
[tex]\implies y=8[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=4(8)[/tex]
[tex]\implies x=32[/tex]
Therefore, Hugo has:
