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Nadia has a handful of coins all of which are either dimes or quarters she has a total of 23 coins in her hand and a total of $3.65 worth of coins let D equal the number of dimes Nadia has and like Q represent the number of quarters she has. Must model the solution and show work.

Nadia has a handful of coins all of which are either dimes or quarters she has a total of 23 coins in her hand and a total of 365 worth of coins let D equal the class=

Respuesta :

Nadia cannot have 18 dimes and 5 quarters.

The equations that represent the question are:

D + Q = 23 equation 1

0.1d + 0.25q = 3.65  equation 2

The number of dimes is 14 and the number of quarters is 9.

Can Nadia have 18 dimes and 5 quarters?

The equation that represents the total amount of money she has is: 0.1d + 0.25q = 3.65

0.1(18) + 0.25(5) = 3.05

$3.05 is less than 3.65

What are the system of equations that models the situation?

D + Q = 23 equation 1

0.1d + 0.25q = 3.65  equation 2

What is the solution to the equation?

Given the above equations, multiply equation 1 by 0.1

0.1d + 0.1q = 2.3 equation 3

Subtract equation 3 from 2

0.15q = 1.35

Divide both sides by 0.15

q = 1.35 / 0.15

q = 9

To determine the value of d, subtract 9 from 23 : 23 - 9 = 14

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

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