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Jacob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out how many of each (quarters and dimes) Jacob has. What do the unknowns in this system represent and what are the two equations that that need to be solved? Finally, solve the system of equations.

Respuesta :

Answer:  The required number of quarters is 23 and that of dimes is 37.

Step-by-step explanation:  Given that Jacob has 60 coins consisting of quarters and dimes and the combined value of the coins is $9.45.

We are to find the number of quarters and dimes.

Let x and y represents the number of quarters and dimes respectively.

Then, according to the given information, we have

[tex]x+y=60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.25x+0.10y=9.45\\\\\Rightarrow 25x+10y=945\\\\\Rightarrow 5x+2y=189~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Multiplying equation (i) by 2, we have

[tex]2(x+y)=2\times60\\\\\Rightarrow 2x+2y=120~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Subtracting equation (iii) from equation (ii), we get

[tex](5x+2y)-(2x+2y)=189-120\\\\\Rightarrow 3x=69\\\\\Rightarrow x=\dfrac{69}{3}\\\\\Rightarrow x=23.[/tex]

And, from equation (i), we get

[tex]23+y=60\\\\\Rightarrow y=60-23\\\\\Rightarrow y=37.[/tex]

Thus, the required number of quarters is 23 and that of dimes is 37.

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