Respuesta :
Answer: nickels = 12, dimes = 8, quarters = 3
Step-by-step explanation:
First, set up the equations for each coin:
[tex]\begin {array}{c|c|c|l}\underline{\quad Type\quad }&\underline{Value}&\underline{Quantity}&\underline{\qquad \qquad \qquad Equation\qquad }\\ Nickel& \$0.05&4+d&0.05(4+d) = 0.20 + 0.05d\\Dime& \$0.10&d&\qquad 0.10(d)=0.10d\\Quarter& \$0.25&d-5&0.25(d-5)=0.25d-1.25\\\end{array}[/tex]
Next, the sum of the coins is $2.15 so substitute and solve for the variable:
Nickels + Dimes + Quarters = Sum
0.20 + 0.05d + 0.10d + 0.25d - 1.25 = 2.15
0.40d - 1.05 = 2.15
0.40d = 3.20
d = 8
Lastly, plug the d-value into the quantity equation for the nickels and quarters to find their quantity.
nickels: 4 + d = 4 + (8) = 12
quarters: d - 5 = (8) - 5 = 3
The number of coins of nickels are [tex]\boxed{12}[/tex], the number of coins of dimes are [tex]\boxed{8}[/tex] and the number of coins of quarters are [tex]\boxed{3}.[/tex]
Further explanation:
Given:
Adam has [tex]\$ 2.15[/tex] in nickels, dimes and quarters.
If the number of dimes is 4 less than the number of nickels, and 5 more than the number of quarters.
Explanation:
Consider the number of coins of nickels as [tex]x[/tex].
Consider the number of coins of dimes as [tex]y[/tex].
Consider the number of coins of quarters as [tex]z[/tex].
The value of nickel in dollar is [tex]\$ 0.05.[/tex]
The value of dime in dollar is [tex]\$ 0.10.[/tex]
The value of quarter in dollar is [tex]\$ 0.25.[/tex]
If the number of dimes is 4 less than the number of nickels
[tex]x = \left( {4 + y} \right)[/tex]
If the number of dimes5 more than the number of quarters
[tex]z = y - 5[/tex]
Adam has [tex]\$ 2.15[/tex] in nickels, dimes and quarters.
[tex]\begin{aligned}0.05x + 0.10y + 0.25z &= 2.15\\0.05\left( {4 + y} \right) + 0.10y + 0.25\left( {y - 5} \right) &= 2.15\\0.40y - 1.05&= 2.15\\0.40y &= 3.20\\y&= 8\\\end{aligned}[/tex]
Number of nickels are 12.
Number of quarters are 3.
The number of coins of nickels are [tex]\boxed{12}[/tex], the number of coins of dimes are [tex]\boxed{8}[/tex] and the number of coins of quarters are [tex]\boxed{3}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomial
Keywords: Adam, $2.15, nickels, dimes, quarters, pocket, number, less, less than, 5 more than, coin, number of quarters.
