15 July, 00:33

# Make an equation and solve!A man has \$0.70 in dimes and nickels. He has 8 coins altogether. How many nickels does he have?

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1. 15 July, 00:56
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The number of nickels he has is 2.

Step-by-step explanation:

A man has \$0.70 consisting of dimes and nickels. He has 8 coin altogether. The number of nickel he has can be calculated below.

let

number of dimes = a

number of nickel = b

a + b = 8 ... (i)

Total cost

1 dime = \$0.1

1 nickel = \$0.05

0.1a + 0.05b = 0.70 ... (ii)

a + b = 8 ... (i)

0.1a + 0.05b = 0.70 ... (ii)

a = 8 - b

insert the value of a in equation (ii)

0.1 (8 - b) + 0.05b = 0.70 ... (ii)

0.8 - 0.1b + 0.05b = 0.70

0.80 - 0.70 = 0.1b - 0.05b

0.1 = 0.05b

divide both sides by 0.05

b = 0.1/0.05

b = 2

Insert the value of b in equation (i)

a + b = 8 ... (i)

a + 2 = 8

a = 8 - 2

a = 6

The number of nickels he has is 2.
2. 15 July, 01:27
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Answer: He has 6 dimes and 2 nickels.

Step-by-step explanation:

If D is the number of dimes and N the number of nickels, we have that:

He has 8 coins:

D + N = 8

He has \$0.70 in total:

D*0.10 + N*0.05 = 0.70

Then we have two equations, now we need to isolate one variable in one of the equations and then replace it in the other, let's isolate D in the first equation:

D = 8 - N

Now we can replace it in the other equation:

(8 - N) * 0.10 + N*0.05 = 0.70

0.80 - N * (0.10 - 0.05) = 0.70

-N*0.05 = 0.70 - 0.80 = - 0.10

N = 0.10/0.05 = 2

D = 8 - N = 8 - 2 = 6

He has 6 dimes and 2 nickels.