Nicole has 16 nickels and dimes. if the value of her coins is 1.05, how many of each coin does she have?

Step-by-step explanation:

If all were dimes, she would have $1.60, which is $0.55 more than she actually has. Replacing a dime with a nickel reduces the total by .05, so there must be .55/.05 = 11 such replacements. This is the number of nickels. The number of dimes makes up the rest of the 16 coins.

Nicole has 11 nickels and 5 dimes.

You can write equations for this several ways. My personal favorite is to use a single variable to represent the number of highest-value coin: d = number of dimes. Then the number of nickels is 16-d and the total value is ...

  0.10d + 0.05(16 -d) = 1.05

  0.05d + 0.80 = 1.05 . . . eliminate parentheses, collect terms

  0.05d = 0.25 . . . . . . . . . subtract 0.80

  d = 0.25/0.05 = 5 . . . . . number of dimes

  16-d = 16-5 = 11 . . . . . . . .number of nickels

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If you let the variable match the number of nickels, the solution looks a lot like the one described in words, above.

  0.05n + 0.10(16 -n) = 1.05

  -0.05n +1.60 = 1.05

  -0.05n = -0.55 . . . . . . . subtract 1.60

  n = -0.55/-0.05 = 11 . . . number of nickels

  16-n = 16-11 = 5 . . . . . . . number of dimes

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Comparing these two solutions, you see that we work with negative numbers in the second solution. The reason for choosing the variable to represent the higher-value coin is to keep the numbers positive, as they are in the first solution. (It's no big deal, if you're not bothered by negative number arithmetic.)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

according to egenuity the answer is

step-by-step explanation:

d. 344.22