Kevin and Randy Muise have a jar containing 46 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.10. How many of each type of coin do they have?

Answers:

24 quarters

22 nickels

Work Shown:

q = number of quarters

n = number of nickels

q+n = 46 coins total which solves to n = 46-q

25q = value of all the quarters in cents

5n = value of all the nickels in cents

25q+5n = value (cents) of all the coins of both types

25q+5n = 710 cents total = $7.10

Apply substitution.

25q+5n = 710

25q+5(46-q) = 710

25q+230-5q = 710

20q+230 = 710

20q = 710-230

20q = 480

q = 480/20

q = 24

They have 24 quarters

This yields 25*q = 25*24 = 600 cents = $6.00 so far.

Use that value of q to find n

n = 46-q

n = 46-24

n = 22

They also have 22 nickels.

They have an additional 5n = 5*22 = 110 cents = $1.10

In total, they have 6.00+1.10 = 7.10 dollars which confirms we have the correct coin counts. Also, q+n = 24+22 = 46.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

hope this : )