Answer:
8, 9, 10
Step-by-step explanation:
three positive consecutive integers
x, x + 1, x + 2
the product of the smallest and the largest is 26 more than six times the middle integer
x(x + 2) = 6(x + 1) + 26
Expand
x^2 + 2x = 6x + 6 + 26
Combine like terms
x^2 + 2x = 6x + 32
Subtract 6x + 32 from both sides
x^2 - 4x - 32 = 0
Factor
(Alternately use the quadratic formula or complete the sqaure)
(x - 8)(x + 4)
x = {-4, 8}
-4 is extraneous because the integers must be positive
x = 8
x + 1 = 9
x + 2 = 10
8, 9, 10
Well use the distributive property
-98=4x-2(5x+13)
Now multiply 2 times 5x+13
-98=4x-10x-26
Now combine like terms
-98=-6x-26
Now get 26 on the other side by adding it to -98
-6x=-72
x=12
Answer:
20 gallons
Step-by-step explanation:
Divide 120 miles by 8 to find miles per gallon
120 ÷ 8 = 15 miles per gallon
Now divide 300 miles by 15 to find number of gallons required
300 ÷ 15 = 20
20 gallons are required for a journey of 300 miles