Respuesta :
Answer:
(i)
Emily's score was 9
(ii)
e = m + 2
Step-by-step explanation:
Let's assume
Emily's score is e
Miguel's score is m
Valerie's score is v
Their combined score is 24
so, we get
[tex]e+m+v=24[/tex]
Emily and Miguel's combined score is twice that of Valerie
we get
[tex]e+m=2v[/tex]
Valerie scored only one more point than Miguel
we get
[tex]v=m+1[/tex]
(i)
we got system of equations as
[tex]e+m+v=24[/tex].............(1)
[tex]e+m=2v[/tex]..................(2)
[tex]v=m+1[/tex]......................(3)
we can plug second equation into first one
[tex]2v+v=24[/tex]
[tex]3v=24[/tex]
[tex]v=8[/tex]
now, we can plug this into second and third equation
[tex]v=m+1[/tex]
we can plug it and find m
[tex]8=m+1[/tex]
[tex]m=7[/tex]
now, we can find e
[tex]e+7=2\times 8[/tex]
[tex]e=9[/tex]
So, Emily's score was 9
(ii)
we got
e=9
m=7
9=7+2
e=m+2
Answer: Emily's score is 9; Equation (D) v = m+1
Step-by-step explanation: To find Emily's score, let's represent each score with their own initials, i.e.: Emily's score is E; Miguel's score is M and Valerie's score is V.
Their combined score is 24, which means:
E + M + V = 24 (1)
Emily and Miguel's combined score is twice of Valerie, in other words:
E + M = 2V (2)
Valerie scored only one point more than Miguel:
V = M + 1 (3)
Substitute (3) into (2):
E + M = 2(M + 1)
E = 2M - M + 2
E = M + 2 (4)
With (3) and (4), use it to substitute into equation (1):
E + M + V = 24
M + 2 + M + M + 1 =24
3M = 21
M = 7
Using M=7 to find E:
E = M + 2
E = 7 + 2
E = 9
Emily's score is 9.
To represent the situation, the correct equation is V = M + 1, which means Valerie's score is 1 more than Miguel, which is exactly what's written in the question.
