Bethany has $3.10 in nickels and dimes. She has a total of 44 coins. What is the value of the nickels Bethany has?

Total value of nickels = $1.30

Step-by-step explanation:

let the number of nickels ($0.05) be "n" and the number of dimes ($0.10) be "d"

given that the total number of coins is 44, we can write :

number of nickels + number of dimes = 44 coins, or

n + d = 44  (rearranging this)

d = 44 - n > (eq 1)

we are also given that the total value of coins she has is $3.10.

Hence we can also write:

total value of nickels + total value of dimes = $3.10   > (eq 2)

we know that the total value of nickels is the value of each nickel x number of nickels = $0.05n

Similarly, the total value of dimes is the value of each dime x number of dimes  = $0.10d

if we substitute these values into eq 2, we get

0.05n + 0.10d = 3.10 > (eq 3)

we can now solve eq 1 and eq 3 by substitution.

substituting eq 1 into eq 3,

0.05n + 0.10d = 3.10

0.05n + 0.10(44-n) = 3.10

0.05n + 4.4 - 0.10n = 3.10

-0.05n + 4.4 = 3.10 (subtract 4.4 from both sides)

-0.05n = 3.10 - 4.4

-0.05n = -1.3  (divide both sides by -0.05)

n = -1.3 / -0.05

n = 26  (i.e she had 25 nickels)

Hence the value of nickels she has (using formula above)

= $0.05n

= $0.05 x 26

= $1.30

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x