+286 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
+26393 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)
+26393 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)
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
