Mathematics, 08.04.2020 20:21, tata64

Shawna found coins worth $4.32. One-fourth of the found coins are pennies and one-sixth are quarters. The number of nickels found is 1.5 times the number of quarters. How many of each coin did Shawna find?

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answered: nevaehkb

There are 48 coins in total.

Shawna found:

12 Pennies.

12 Nickels.

16 Dimes.

And 8 Quarters.

Step-by-step explanation:

We will let denote the total amount of coins.

We know that the total worth of the coins were $4.32.

One-fourth of the found coins are pennies. Hence:

$\displaystyle \frac{1}{4}x\text{ are pennies.}$

Since pennies are worth $0.01 each, the worth will be:

$\displaystyle \frac{1}{4}x(0.01)$

Similarly, we know that one-sixth of the found coins are quarters. Quarter are worth $0.25. So, the total worth in quarters is:

$\displaystyle \frac{1}{6}x(0.25)$

We have 1.5 times as many nickels as quarters. Therefore, the amount of nickels we have is:

$\displaystyle 1.5(\frac{1}{6}x)=\frac{3}{2}(\frac{1}{6}x)=\frac{1}{4}x$

Or one-fourth of the total amount.

Since each nickel is worth $0.05, the total worth in nickels is:

$\displaystyle \frac{1}{4}x(0.05)$

We will now need to determine the amount to dimes. Notice that 1/4 of the total amount of coins were pennies, 1/6 were quarters, and another 1/4 were nickels. Therefore, the amount of coins that were dimes n must be the remaining fraction of the total amount of coins. In other words, the fraction that were dimes is:

$\displaystyle n=100\%-\frac{1}{4}-\frac{1}{6}-\frac{1}{4}$

Evaluate for n. Let 100% equal 1. Hence:

$\displaystyle \begin{aligned} n&=1-\frac{1}{4}-\frac{1}{6}-\frac{1}{4} \\ &=\frac{12}{12}-\frac{3}{12}-\frac{2}{12}-\frac{3}{12}\\&=\frac{12-3-2-3}{12}\\&=\frac{4}{12}=\frac{1}{3} \end{aligned}$

Therefore, 1/3 of the coins were dimes.

Since dimes are worth $0.10, the total worth in dimes are:

$\displaystyle \frac{1}{3}x(0.1)$

The total worth of all the coins found was worth $4.32. Therefore:

$\displaystyle \frac{1}{4}x(0.01)+\frac{1}{6}x(0.25)+\frac{1}{4}x(0.05)+\frac{1}{3}x(0.1)=4.32$

Solve for , the total amount of coins. First, let’s multiply everything by 100 to remove the decimals. Hence:

$\displaystyle 100(\frac{1}{4}x(0.01)+\frac{1}{6}x(0.25)+\frac{1}{4}x(0.05)+\frac{1}{3}x(0.1))=100(4.32)$

Distribute:

$\displaystyle \frac{1}{4}(1)x+\frac{1}{6}(25)x+\frac{1}{4}(5)x+\frac{1}{3}(10)x=432$

Now, let’s multiply everything by 12 to remove the fractions. 12 is the LCM of 4, 6, and 3. Hence:

$\displaystyle 12(\frac{1}{4}(1)x+\frac{1}{6}(25)x+\frac{1}{4}(5)x+\frac{1}{3}(10)x)=12(432)$

Distribute:

3(1)x+2(25)x+3(5)x+4(10)x=5184

Multiply:

3x+50x+15x+40x=5184

Combine like terms:

108x=5184

Divide both sides by 108. Hence, the total amount of coins are:

x=48

1/4 of the total coins are pennies. Hence, there are 1/4(48) or 12 pennies.

1/6 of the total coins are quarters. Hence, there are 1/6(48) or 8 quarters.

As we determined, 1/4 of the total coins are also nickels. Hence, there are 1/4(48) or 12 nickels.

Finally, as we determined, 1/3 of the total coins are dimes. Hence, there are 1/3(48) or 16 times.

answered: Guest

step-by-step explanation:

answered: Guest

step-by-step explanation:

the word superfluous means unnecessary

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Shawna found coins worth $4.32. One-fourth of the found coins are pennies and one-sixth are quarters...