Answer:
18 pounds
Step-by-step explanation:
write a proportion 174/29=108/x and that equals 174x=3132 which then x equals 18
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:
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number y if 2/5of y is 22