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Please help with number 5 I tried it but I’m very confused :(

Please Help With Number 5 I Tried It But Im Very Confused class=

Sagot :

eunice1234

Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

angstar4
Create a system of equations
n + d = 24
0.05n + 0.1d = 1.95

I used substitution
n = 24 - d
0.05(24 - d) + 0.1d = 1.95
1.2 - 0.05d + 0.1d = 1.95
1.2 + 0.05d = 1.95
0.05d = 0.75
d = 15 or 15 dimes

Plug in
n + d = 24
n + 15 = 24
n = 9 or 9 nickels

Check
0.05n + 0.1d = 1.95
0.05(9) + 0.1(15) = 1.95
0.45 + 1.50 = 1.95
1.95 = 1.95
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