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A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How

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by BTGmoderatorDC » Tue Jan 28, 2020 6:40 pm
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11



OA B

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Re: A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. Ho

by deloitte247 » Sat Feb 01, 2020 10:19 pm
Let the number of 10-cent coins = x
Let the number of 25-cent coins = y
Collection of x and y make 16 coins
$$x+y=16........eqn\ i$$
$$x=16-y.............eqn\ ii$$

x of 10-cent coins and y of 25 cent coins has a total face value of $2.35
Total face value in cents=$2.35*100=235cents
$$10x+25y=235$$
Where x=16-y from eqnii
$$10\left(16-y\right)+25y=235$$
$$160-10y+25y=235$$
$$25y-10y=235-160$$
$$15y=75$$
$$\frac{15y}{15}=\frac{75}{15}$$
$$y=5$$
There are five coins with face value of 25cents

$$answer\ is\ Option\ B$$
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