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Jlenok [28]
4 years ago
15

Place 20 pennies in a row on a table. Replace every fourth coin with a nickle. Now replace every third coin with a dime. Then re

place every sixth coin with a quarter. What is the value of the 20 coins now on the table?
Mathematics
1 answer:
inna [77]4 years ago
6 0

Answer: $1.35

Step-by-step explanation:

Changing every fourth coin to a nickle will give you 5 nickles because 20/4 is 5. Then replacing every third coin with a dime will give you 6 dimes. Then finally every sixth coin with a quarter will give you 3 quarters. However there is some overlap where you are replacing a nickle with a dime or a dime with a quarter so it ends up being 3 quarters, 3 dimes, and 4 nickles with the rest being pennies.

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Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8
goblinko [34]
\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y  = \frac{17}{14} } \atop {x+7y=8}} \right.

To solve this system by substitution, first isolate x in the second equation.

x+7y=8
x+7y-7y=8-7y
x=8-7y

Now, plug this expression (8-7y) for x in the top equation to solve for y.

\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}
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72-63y+8y=17
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Now that you have y, plug it into the second equation and solve for x.

x+7y=8
x+7(1)=8
x+7=8
x=1

Last step is to plug your x- and y-values in to both equations to check your work.

\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}

\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ;  \frac{1}{3} * \frac{8}{8} = \frac{8}{24}

\frac{9}{24} + \frac{8}{24} = \frac{17}{24}  <--True

1+7(1)=8
1+7=8   <--True

Answer:
x=1 \\ y=1
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