A box contains 81 coins, only dimes and nickels. The amount of money in the box is $5.30. How many dimes and how many nickels are in the box?
The number of dimes is
The number of nickels is

Step-by-step explanation:

Let d represent the number of dimes. Then 81-d is the number of nickels and the total value in cents is ...

  10d +5(81-d) = 530

  5d +405 = 530 . . . eliminate parentheses

  d +81 = 106 . . . . . divide by 5

  d = 25 . . . . . . . . . subtract 81; number of dimes

  81 -d = 81 -25 = 56 . . . . . number of nickels

There are 25 dimes and 56 nickels in the box.

Comment on the method of solution

It usually works well to let the variable represent the amount of the highest-value contributor (dimes). This keeps the numbers positive as the solution progresses.

answer: 12/52

step-by-step explanation: my reasoning is that there are 12 face cards in a deck and a total of 52 cards in all.

b: y = 2x + 2

step-by-step explanation:

y = 2x + 1

we want a line that is parallel, so it will have the same slope

the line is in the form y= mx+b, so the slope is 2

we have a slope and the y intercept (0,2)

since x is 0 we know the y point which is the y intercept

we can use y= mx+b to write the equation of the line

m is the slope and b is the y intercept

y = 2x +2