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if I climb with my mother on a scale I weighed 103kg, and if I get on with my father, 113kg. If my father and mother together weigh 126kg, how many kilos do the three of us weigh all together?

 

A)168       B)169       C)170     D)171      E)172

 Nov 18, 2015

Best Answer 

 #1
avatar+26364 
+15

if I climb with my mother on a scale I weighed 103kg, and if I get on with my father, 113kg. If my father and mother together weigh 126kg, how many kilos do the three of us weigh all together?

 

A)168       B)169       C)170     D)171      E)172


\(\small{ \begin{array}{lrcll} (1) & i + \text{ mother } &=& 103\ \text{kg} \\ (2) & i + \text{ father } &=& 113\ \text{kg} \\ (3) & \text{ father }+\text{ mother } &=& 126\ \text{kg} \\ \hline (1)+(2)+(3) & (i + \text{ mother }) + (i+ \text{ father }) + (\text{ father }+\text{ mother }) &=& 103\ \text{kg} + 113\ \text{kg} + 126\ \text{kg}\\ & 2\cdot i + 2\cdot \text{ mother } + 2\cdot \text{ father } &=& 103\ \text{kg} + 113\ \text{kg} + 126\ \text{kg}\\ & 2\cdot i + 2\cdot \text{ mother } + 2\cdot \text{ father } &=& 342\ \text{kg}\\ & 2\cdot( i + \text{ mother } + \text{ father } ) &=& 342\ \text{kg}\\ & i + \text{ mother } + \text{ father } &=& \frac{ 342 } { 2 } \ \text{kg}\\ & \mathbf{ i + \text{ mother } + \text{ father } }& \mathbf{=} & \mathbf{ 171\ \text{kg} }\\ \end{array} }\)

 

The three of us weight all together 171 kg

 

The answer is D)

 

laugh

 Nov 18, 2015
 #1
avatar+26364 
+15
Best Answer

if I climb with my mother on a scale I weighed 103kg, and if I get on with my father, 113kg. If my father and mother together weigh 126kg, how many kilos do the three of us weigh all together?

 

A)168       B)169       C)170     D)171      E)172


\(\small{ \begin{array}{lrcll} (1) & i + \text{ mother } &=& 103\ \text{kg} \\ (2) & i + \text{ father } &=& 113\ \text{kg} \\ (3) & \text{ father }+\text{ mother } &=& 126\ \text{kg} \\ \hline (1)+(2)+(3) & (i + \text{ mother }) + (i+ \text{ father }) + (\text{ father }+\text{ mother }) &=& 103\ \text{kg} + 113\ \text{kg} + 126\ \text{kg}\\ & 2\cdot i + 2\cdot \text{ mother } + 2\cdot \text{ father } &=& 103\ \text{kg} + 113\ \text{kg} + 126\ \text{kg}\\ & 2\cdot i + 2\cdot \text{ mother } + 2\cdot \text{ father } &=& 342\ \text{kg}\\ & 2\cdot( i + \text{ mother } + \text{ father } ) &=& 342\ \text{kg}\\ & i + \text{ mother } + \text{ father } &=& \frac{ 342 } { 2 } \ \text{kg}\\ & \mathbf{ i + \text{ mother } + \text{ father } }& \mathbf{=} & \mathbf{ 171\ \text{kg} }\\ \end{array} }\)

 

The three of us weight all together 171 kg

 

The answer is D)

 

laugh

heureka Nov 18, 2015
 #2
avatar+286 
+5

Thanks

 Nov 18, 2015
 #3
avatar
+5

if I climb with my mother on a scale I weighed 103kg, and if I get on with my father, 113kg. If my father and mother together weigh 126kg, how many kilos do the three of us weigh all together?


s=son

m=mother

f=father

s+m=103, s+f=113, m+f=126

 

Solve the following system:
{m+s = 103 |     (equation 1)
f+s = 113 |     (equation 2)
f+m = 126 |     (equation 3)
Swap equation 1 with equation 2:
{f+0 m+s = 113 |     (equation 1)
0 f+m+s = 103 |     (equation 2)
f+m+0 s = 126 |     (equation 3)
Subtract equation 1 from equation 3:
{f+0 m+s = 113 |     (equation 1)
0 f+m+s = 103 |     (equation 2)
0 f+m-s = 13 |     (equation 3)
Subtract equation 2 from equation 3:
{f+0 m+s = 113 |     (equation 1)
0 f+m+s = 103 |     (equation 2)
0 f+0 m-2 s = -90 |     (equation 3)
Divide equation 3 by -2:
{f+0 m+s = 113 |     (equation 1)
0 f+m+s = 103 |     (equation 2)
0 f+0 m+s = 45 |     (equation 3)
Subtract equation 3 from equation 2:
{f+0 m+s = 113 |     (equation 1)
0 f+m+0 s = 58 |     (equation 2)
0 f+0 m+s = 45 |     (equation 3)
Subtract equation 3 from equation 1:
{f+0 m+0 s = 68 |     (equation 1)
0 f+m+0 s = 58 |     (equation 2)
0 f+0 m+s = 45 |     (equation 3)
Collect results:
ANSWER 
|  f = 68              SUM OF ALL AGES=171
 m = 58
  s = 45

 Nov 18, 2015
 #4
avatar
+5

Well....

103 + 113  - 126 = 2(you)      Since you were weighed twice.

you = 45

 

M + D = 126 (given)    then add you   126 + 45 = 171

 Nov 18, 2015

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