by Visticious Loverial
(Austria)
The sum of four numbers a, b, c, and d is 68. If we increase a by 7, we get x. If we increased b by 8, we get x. If we decrease c by 15, we get 2x.If we multiply d by 4, we get x. What is the value of x?
Solution
The problem gives the following 5 equations
a + b + a + d = 68 (1)
a + 7 = x (2)
b + 8 = x (3)
c - 15 = 2x (4)
d x 4 = x (5)
Use equations (2),(3), (4),and (5) to solve for a, b, c, and d.
a + 7 = x
a + 7 - 7 = x - 7
a = x - 7
b + 8 = x
b + 8 - 8 = x - 8
b = x - 8
c - 15 = 2x
c - 15 + 15 = 2x + 15
c = 2x + 15
d x 4 = x
(d x 4)/4 = x / 4
d = x / 4
Replace a, b, c, and d into equation (1)
x - 7 + x - 8 + 2x + 15 + x / 4 = 68
x + x + 2x - 7 - 8 + 15 + x / 4 = 68
4x - 15 + 15 + x / 4 = 68
4x + x / 4 = 68
Multiply everything by 4
4 times 4x + 4 times (x / 4) + 4 times 68
16x + x = 272
17x = 272
Since 17 x 16 = 272, x = 16
Mar 19, 18 05:53 PM
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Mar 19, 18 05:53 PM
Triangle midsegment theorem proof using coordinate geometry and algebra
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