8 - (7/10)t = 6 - (1/5)t

t = 4

Step-by-step explanation:

Solve for t:

8 - (7 t)/10 = 6 - t/5

Hint: | Put the fractions in 8 - (7 t)/10 over a common denominator.

Put each term in 8 - (7 t)/10 over the common denominator 10: 8 - (7 t)/10 = 80/10 - (7 t)/10:

80/10 - (7 t)/10 = 6 - t/5

Hint: | Combine 80/10 - (7 t)/10 into a single fraction.

80/10 - (7 t)/10 = (80 - 7 t)/10:

1/10 (80 - 7 t) = 6 - t/5

Hint: | Put the fractions in 6 - t/5 over a common denominator.

Put each term in 6 - t/5 over the common denominator 5: 6 - t/5 = 30/5 - t/5:

(80 - 7 t)/10 = 30/5 - t/5

Hint: | Combine 30/5 - t/5 into a single fraction.

30/5 - t/5 = (30 - t)/5:

(80 - 7 t)/10 = (30 - t)/5

Hint: | Make (80 - 7 t)/10 = (30 - t)/5 simpler by multiplying both sides by a constant.

Multiply both sides by 10:

(10 (80 - 7 t))/10 = (10 (30 - t))/5

Hint: | Cancel common terms in the numerator and denominator of (10 (80 - 7 t))/10.

(10 (80 - 7 t))/10 = 10/10×(80 - 7 t) = 80 - 7 t:

80 - 7 t = (10 (30 - t))/5

Hint: | In (10 (30 - t))/5, divide 10 in the numerator by 5 in the denominator.

10/5 = (5×2)/5 = 2:

80 - 7 t = 2 (30 - t)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

80 - 7 t = 60 - 2 t

Hint: | Move terms with t to the left hand side.

Add 2 t to both sides:

2 t - 7 t + 80 = (2 t - 2 t) + 60

Hint: | Look for the difference of two identical terms.

2 t - 2 t = 0:

2 t - 7 t + 80 = 60

Hint: | Group like terms in 2 t - 7 t + 80.

Grouping like terms, 2 t - 7 t + 80 = 80 + (2 t - 7 t):

80 + (2 t - 7 t) = 60

Hint: | Combine like terms in 2 t - 7 t.

2 t - 7 t = -5 t:

-5 t + 80 = 60

Hint: | Isolate terms with t to the left hand side.

Subtract 80 from both sides:

(80 - 80) - 5 t = 60 - 80

Hint: | Look for the difference of two identical terms.

80 - 80 = 0:

-5 t = 60 - 80

Hint: | Evaluate 60 - 80.

60 - 80 = -20:

-5 t = -20

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -5 t = -20 by -5:

(-5 t)/(-5) = (-20)/(-5)

Hint: | Any nonzero number divided by itself is one.

(-5)/(-5) = 1:

t = (-20)/(-5)

Hint: | Reduce (-20)/(-5) to lowest terms. Start by finding the GCD of -20 and -5.

The gcd of -20 and -5 is -5, so (-20)/(-5) = (-5×4)/(-5×1) = (-5)/(-5)×4 = 4:

t = 4

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

they used 313 gallons of paint