A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?

On Solving  equation in one variable 0.4x = 5.2, we found that the clerk returned 13 dimes, 34 quarters and4 nickels in change of $10 bill.

What is an linear equation in one variable?

Linear equation is an equation containing one variable with power one and constants.

Standard form of an linear equation in one variable x is :

ax + b= 0 ,  a, b are constants

x= -b/ a is solution if this equation. Linear equation can be solved by adding or subtracting , multiplying , division same number to both sides.

A clerk need a change of $10 bill

Let the clerk returned x dimes and y nickels and z quarters to pay $10

Value of one nickel =  $ 0.05, one dime = $ 0, one quarter = $ 0.25

Value of x dimes becomes 0.1x

Value of y nickels  becomes 0.05 y

value of z quarters becomes  0.25 z

Total value of given dimes, quarters and nickels , 0.1 x + 0.05 y + 0.25z = 10

Number of dimes = Number of nickels + 9

∴ x = y +9 ⇒ y = x- 9

Number of quarters = Number of dimes +21

∴ z = x + 21  

Put y = x-9 and z = x + 21   in 0.1 x + 0.05 y + 0.25z = 10

Then,

0.1 x + 0.05 ( x-9) + 0.25 (x +21) = 10

⇒ 0.1 x +0.05x -0.45 + 0.25 x + 5.25 = 10

⇒ 0.4x +4.8 = 10

⇒ 0.4 x = 10- 4.8

⇒ 0.4x = 5.2

⇒ x = 5.2/0.4 = 13

Thus , y = x-9 = 13 -9 = 4

z = x + 21 = 13 + 21 = 34

Therefore, the clerk returned 13 dimes , 4 nickels and 34 quarters for $10 bill.

Also, learn more about linear equation from the link below:

brainly.com/question/24145091

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