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17 Adam has $2.15 in nickels, dimes and quarters in his pocket. If the number of dimes is 4 less than the number of nickels, and 5 more than the number of quarters, then how many of each type of coin does he have?

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tramserran

Answer: 12 nickels, 8 dimes, 3 quarters

Step-by-step explanation:

[tex]\begin {array}{l|c|c||l}&\underline{Value}&\underline{Quantity}&\underline{\qquad Total\ Value\qquad }\\ Nickels&\$ 0.05&4+d&0.05(4+d)=0.20+0.05d\\Dimes&\$ 0.10&d&\qquad 0.10(d)=0.10d\\Quarters&\$ 0.25&d-5&0.25(d-5)=0.25d-1.25\\\end{array}[/tex]

    Nickels     + Dimes +  Quarters   = Total

0.20 + 0.05d + 0.10d + 0.25d - 1.25 = 2.15

                                       0.40d - 1.05 = 2.15

                                       0.40d           = 3.20

                                               d            = 8

Nickels: 4 + d   = 4 + (8)   = 12

Quarters: d - 5   = (8) - 5   = 3


Check:

Nickels:   0.05(12)  = $0.60

Dimes:     0.10 (8)   = $0.80

Quarters: 0.25(3)   = $0.75

                Total:     = $2.15   [tex]\checkmark[/tex]

There are [tex]\boxed{12{\text{ nickel coins}}}, \boxed{8{\text{ dime coins}}}[/tex] and [tex]\boxed{3{\text{ quarter coins}}}.[/tex]

Further explanation:

Given:

Adam has [tex]\$ 2.15[/tex] in nickels, dimes and quarters.

Explanation:

Let us consider the number of coins of nickels as [tex]\text{x}[/tex], the number of coins of dimes as [tex]\text{y}[/tex] and the number of coins of quarters are [tex]\text{z}[/tex].

[tex]\boxed{1{\text{ nickel}} = \$ 0.05}.[/tex]

[tex]\boxed{1{\text{ dime}} = \$ 0.05}.[/tex]

[tex]\boxed{1{\text{ quarter}} = \$ 0.05}.[/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 dimes 5 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 coins of nickels are 12.

Number of coins of quarters are 3.

There are [tex]\boxed{12{\text{ nickel coins}}}, \boxed{8{\text{ dime coins}}}[/tex] and [tex]\boxed{3{\text{ quarter coins}}}.[/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.

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