Answer: The numbers are: " 21 " and " 105 " .
___________________________________________________
Explanation:
___________________________________________________
Let "x" be the "one positive number:
Let "y" be the "[an]othyer number".
x = 1/5 (y)
___________________________________________________
Given that the difference of the two number is "84" ; and that "x" is (1/5) of "y" ; we determine that "x" is smaller than "y".
So, y − x = 84 .
Add "x" to each side of this equation; to solve for "y" in terms of "x" ;
y − x + x = 84 + x ;
y = 84 + x ;
___________________________________________________
So, we have:
x = (1/5) y ;
and: y = 84 + x ;
Substitute "(1/5)y" for "x" ; in "y = 84 + x " ; to solve for "y" ;
y = 84 + [ (1/5)y ]
Subtract " [ (1/5)y ] " from EACH SIDE of the equation ;
y − [ (1/5)y ] = 84 + [ (1/5)y ] − [ (1/5)y ] ;
to get:
[ (4/5)y ] = 84 ;
↔ (4y) / 5 = 84 ;
→ 4y = 5 * 84 ;
Divide EACH SIDE of the equation by "4" ;
to isolate "y" on one side of the equation; and to solve for "y" ;
4y / 4 = (5 * 84) / 4 ;
y = 5 * (84/4) = 5 * 21 = 105 .
y = 105 .
___________________________________________________
Now, plug "105" for "y" into:
___________________________________________________
Either:
___________________________________________________
x = (1/5) y ;
OR:
y = 84 + x ;
___________________________________________________
to solve for "x" ;
___________________________________________________
Let us do so in BOTH equations; to see if we get the same value for "x" ; which is a method to "double check" our answer ;
___________________________________________________
Start with:
x = (1/5)y
→ (1/5)*(105) = 105 / 5 = 21 ; x = 21 ;
___________________________________________________
So, x = 21; y = 105 .
___________________________________________________
Now, let us see if this values hold true in the other equation:
___________________________________________________
y = 84 + x ;
105 = ? 84 + 21 ?
105 = ? 105 ? Yes!
___________________________________________________
The numbers are: " 21 " and "105 " .
___________________________________________________
Most of the information's that are required for solving the problem is already given in the question. So it is very important to read the question minutely before going for solving and getting to the desired answer.
Total number of eggs that Mary has = 216
Number of eggs that can fit in each carton = 12
Then
Number of cartons required to completely fill = 216/12
= 18
So 18 cartons are required by Mary to fill all the eggs that she has. I hope the procedure is simple enough for you to understand. You can always use this method for solving similar questions in future without requiring any kind of additional help from anybody.
Answer:
Step-by-step explanation:
Both the numerator and denominator of the fraction 
share a common factor of 2, so you can divide the fraction by 
(1). This leaves you with:
÷ = 
This means that the fraction .
Answer:
160 m²
Step-by-step explanation:
The surface area of the prism is the sum of the area of its surfaces. This prism has 5 surfaces, namely the front, back, right, left and bottom surface.
<u>Area of front surface</u>
Area of triangle= ½ ×base ×height
Base= 6 m
Height= 4 m
Area= 6(4)= 24 m²
<u>Area of back </u><u>surface</u>
Area of back surface
= area of front surface
= 24 m²
<u>Area of right </u><u>surface</u>
Area of rectangle= length ×breadth
Length= 7 m
Breadth= 5 m
Area= 7(5)= 35 m²
<u>Area of left </u><u>surface</u>
Area of left surface
= area of right surface
= 35 m²
<u>Area of bottom </u><u>surface</u> (base of prism)
Area of rectangle= length ×breadth
Length= 7 m
Breadth= 6 m
Area= 6(7)= 42 m²
The total surface area can be found by adding all of the surface areas we have found earlier.
Total surface area
= 24 +24 +35 +35 +42
= 160 m²
