Question

I WILL MARK BRAINLIEST TO THE PERSON WITH THE BRAINLIEST ANSWER!! PLEASE ANSWER ALL QUESTIONS AND SHOW FULL SOLUTIONS. PLEASE SHOW ALL THE WORK NEEDED. THANK YOU.

Answer 1

Answer:

Number 7 (I DONT KNOW THE OTHER ONES)

Step-by-step explanation:

Answer:

There are 19 quarters and 8 dimes.

Step-by-step explanation:

We will let x denote the amount of quarters.

Since there are 27 coins in total, (27-x) will be the amount of dimes there are.

Since each quarter is worth $0.25, the total value of quarters is given by 0.25x.

And since each dime is worth $0.10, the total value of dimes is given by 0.1(27-x).

We know that the total value of all 27 coins is $5.55. So, we can write the following equation:

So, we will determine the value of x, the amount of quarters there are.  

First, let’s multiply everything by 100 to remove the decimals. So:

(Distribute)

(Distribute)

(Combine like terms)

(Subtract 270 from both sides)

(Divide both sides by 15)

So, the value of x is 19.

This means that there are 19 quarters.

So, the amount of dimes must be 27-19 or 8 dimes.

Answer 2

9514 1404 393

Answer:

  1a) x = 4

  1c) x = 6

  1d) x = 10

  1f) x = -42

Step-by-step explanation:

1a) 3x -8 = 4

This is a "two step" equation with a variable term and constant on the same side of the equal sign. Step 1, add the opposite of that constant to both sides of the equation:

  3x = 12

Step 2: divide both sides of the equation by the coefficient of the variable:

  x = 4

__

1c) This is similar to 1a, except that it has variables on both sides of the equal sign. Find the variable term with the smallest coefficient. Here, it is -x, because the coefficient -1 is less than 2. Add the opposite of that term to both sides of the equation:

  3x -8 = 10

Now, you have a 2-step equation in the same form as 1a. Solve it the same way.

  3x = 18 . . . . add 8

  x = 6 . . . . . . divide by 3

Check

  2(6) -8 = 10 -(6)

  12 -8 = 10 -6

  4 = 4 . . . . . true; answer is correct

__

1d) After you eliminate parentheses using the distributive property, you end up with a 3-step equation as in 1c.

  6x -12 = 3x +2x -2

  6x -12 = 5x -2 . . . . . . combine like terms. (5x is the smallest x-term)

  x -12 = -2 . . . . . . . . . subtract 5x

  x = 10 . . . . . . . . . . . . add 12

Check

  6(10 -2) = 3(10) +2(10 -1)

  6(8) = 30 +2(9)

  48 = 30 +18

  48 = 48 . . . . true; answer is correct

__

1f) You can work this as is using the fractional coefficients. Most folks prefer to "clear fractions" first. To do that, you need to find the least common denominator and multiply both sides of the equation by it. The least common denominator of 1/3 and 1/2 is 6.

  2x = 3x +42 . . . . . multiply both sides by 6

  0 = x + 42 . . . . . . . subtract the smallest x-term from both sides

  -42 = x . . . . . . . . . add -42

Check

  (-42)/3 = (-42)/2 +7

  -14 = -21 +7

  -14 = -14 . . . . . . . true; answer is correct

___

If you work this using the given coefficients, you can subtract 1/3x to get ...

  0 = x/6 +7

  -7 = x/6 . . . . . subtract 7

  -42 = x . . . . . . multiply by 6

You notice that we had to multiply by 6 in the solution process anyway. Doing that first makes the fractions go away, so is often the preferred solution method.