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Let x and y be the two numbers. 1) x + y = 19
2) xy = 78
Solve (1) for y. Subtract x from both sides.
y = 19 - x
Then we can write equation (2) as x(19-x)=78
Simplifying
x(19 + -1x) = 78
(19 * x + -1x * x) = 78
(19x + -1x2) = 78
Solving
19x + -1x2 = 78
Solving for variable 'x'.
Reorder the terms:
-78 + 19x + -1x2 = 78 + -78
Combine like terms: 78 + -78 = 0
-78 + 19x + -1x2 = 0
Factor a trinomial.
(-13 + x)(6 + -1x) = 0
==
Set the factor '(-13 + x)' equal to zero and attempt to solve:
Simplifying
-13 + x = 0
Solving
-13 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13
Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13
Combine like terms: 0 + 13 = 13
x = 13
Simplifying
x = 13
==
Set the factor '(6 + -1x)' equal to zero and attempt to solve:
Simplifying
6 + -1x = 0
Solving
6 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6
Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6
Combine like terms: 0 + -6 = -6
-1x = -6
Divide each side by '-1'.
x = 6
Simplifying
x = 6
==
x = {13, 6} The answer to your question is that the larger number is 13.
10 cm
Perimeter is 100', so each side = 25' and 25 squared = 625. QED
30
16
lenght=15, width= 10
15
14 cm
the answer is 6
7 feet
2(7+2) = 18 feet
7*2 = 14 square feet
3 and 5
4
Improved Answer:-
30 feet of fencing will be needed
5
5+4 = 9
52+42 = 41
Let the length be 2x and the width be x:
length*width = area
2x*x = 50
2x2 = 50
x2 = 25
x = 5 feet
A = area, L = length, W = width
A = LW
L = 2W
A = (2W)W = 2W2
2W2 = 50
W = 5 ft
The width is either 2ft or 7ft.
7
The two numbers are 6 and 13 so therefore the smaller number is 6
