Find the two-digit number satisfying the following two conditions: 1) four times the units digit is six less than twice the tens digit. 2) the number is nine less than three times the number obtained by reversing the digits.

Define x :

Let the two digit number be 10x + y.


Construct Equation :

Four times the units digit is six less than twice the tens digit
⇒ 4y = 2x - 6
⇒2y = x - 3
⇒ x = 2y + 3

The number is nine less than three times the number obtained by reversing the digits.
⇒10x + y = 3(10y + x) - 9
⇒ 10x + y = 30y + 3x - 9
⇒ 7x = 29y - 9


Solve for x and y :

 x = 2y + 3 (1)
10x = 29y - 9  (2)

Sub (1) into (2) :

7(2y + 3) = 29y - 9
14y + 21 = 29y - 9
15y = 30
y = 2 Sub into (1)
x = 2(2) + 3
x = 7


Find the number:

Number = 10x + y = 10(2) + 7 = 27


The 2-digit number is 27.

She will need 5/8 bags for each square yard.

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.