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There is a jar of nickels and dimes on the kitchen counter. There are 60 coins in the jar; when counted, they have a total value of $5.40. determine how many dimes are in the jar.

Sagot :

olumideolawoyin

Answer:

48

Step-by-step explanation:

Let the value of a nickel (n) be $0.05 and the value of a dime (d) be $0.10

If there are 60 coins in the jar:

n + d = 60 ... (1)

A nickel is worth = $0.05 and a dime is worth $0.10 and if the total value of all the coins is $5.40 then:

0.05n + 0.10d = 5.40 ... (2)

Make n the subject in (1)

n = 60 - d ... (3) then

Substitute equation (3) in (2)

0.05(60 - d) + 0.10d = 5.40

3 - 0.05d + 0.10d = 5.40

0.05d = 5.40 - 3 Divide both sides by 0.05

d = 2.4 / 0.05

d = 48

Hence, the number of dimes in the jar are 48.

semsee45

Answer:

48 dimes

Step-by-step explanation:

To determine how many dimes are in the jar, we can create and solve a system of equations.

Let n be the number of nickels in the jar.

Let d be the number of dimes in the jar.

Given that there are a total of 60 coins in the jar, this can be expressed as:

[tex]n + d = 60[/tex]

A nickel has the value of $0.05, and a dime has the value of $0.10. Given that the total value of the coins is $5.40, then:

[tex]0.05n + 0.10d = 5.40[/tex]

Therefore, the system of equations that represents the given scenario is:

[tex]\begin{cases} n + d = 60\\0.05n + 0.10d = 5.40\end{cases}[/tex]

To solve, rearrange the first equation to isolate n:

[tex]n = 60 - d[/tex]

Now, substitute this into the second equation and solve for d:

[tex]0.05(60-d)+0.10d=5.40 \\\\ 0.05(60-d)+0.10d=5.40 \\\\ 3-0.05d+0.10d=5.40 \\\\ 3+0.05d=5.40 \\\\ 0.05d = 5.40 - 3 \\\\ 0.05d = 2.40 \\\\ d=\dfrac{2.40}{0.05} \\\\ d=48[/tex]

Therefore, the number of dimes in the jar is:

[tex]\LARGE\boxed{\boxed{ \sf 48 \; dimes}}[/tex]

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