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Jessica has 48 coins, some of them are nickels and some are dimes. How many of each does she have if she has $3.25 total? 69 POINTS





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alinakincsem

Answer:

Nickels = 44.6

Dimes = 3.4

Step-by-step explanation:

We know that Jessica has 48 coins of which some are nickels and some are dimes so we can write it as:

n = amount of nickels

d = amount of dimes

[tex]n+d=48[/tex] --- (1)

We are to find the number of nickels and dimes if their total worth is $3.25.

Since a dime is worth 10¢ and a nickel is 5¢, so it should be:

[tex]0.05n + 0.3d = 3.25[/tex] --- (2)

From (1):

[tex]n=48-d[/tex]

Substituting this value of [tex]n[/tex] in (2) to get:

[tex]0.05(48-d) + 0.3d = 3.25[/tex]

[tex]2.4-0.05d+0.3d=3.25[/tex]

[tex]2.4+0.25d=3.25[/tex]

[tex]0.25d=0.85[/tex]

[tex]d=3.4[/tex]

Finding [tex]n[/tex] by substituting the value of [tex]d[/tex]:

[tex]n=48-d[/tex]

[tex]n=48-3.4[/tex]

[tex]n=44.6[/tex]

Answer:

31 nickels and 17 dimes.

Step-by-step explanation:

Le d represent number of dimes and n represent number of nickels.

We have been given that Jessica has 48 coins, some of them are nickels and some are dimes. We can represent this information in an equation as:

[tex]d+n=48...(1)[/tex]

The coins are worth $3.25. We can represent this information in an equation as:

[tex]0.10d+0.05n=3.25...(2)[/tex]

Form equation (1) we will get,

[tex]d=48-n[/tex]

Substituting this value in equation (2) we will get,

[tex]0.10(48-n)+0.05n=3.25[/tex]

[tex]4.8-0.10n+0.05n=3.25[/tex]

[tex]4.8-0.05n=3.25[/tex]

[tex]4.8-4.8-0.05n=3.25-4.8[/tex]

[tex]-0.05n=-1.55[/tex]

[tex]\frac{-0.05n}{-0.05}=\frac{-1.55}{-0.05}[/tex]

[tex]n=31[/tex]

Therefore, Jessica has 31 nickels.

Substituting [tex]n=31[/tex] in equation (1) we will get,

[tex]d+31=48[/tex]

[tex]d+31-31=48-31[/tex]

[tex]d=17[/tex]

Therefore, Jessica has 17 dimes.

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