Question

The three finalists in the talent show are Emily, Miguel, and Valerie. Their combined score is 24. Emily and Miguel's combined score is twice that of Valerie, and Valerie scored only one more point than Miguel. How many points did Emily score? Which equation is needed to represent the situation? A) e = m + 1 B) m = e + 1 C) m = v + 1 D) v = m + 1

Answer 1

(i)

Emily's score was 9

(ii)

e = m + 2

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

`e+m+v=24`

Emily and Miguel's combined score is twice that of Valerie

we get

`e+m=2v`

Valerie scored only one more point than Miguel

we get

`v=m+1`

(i)

we got system of equations as

`e+m+v=24`.............(1)

`e+m=2v`..................(2)

`v=m+1`......................(3)

we can plug second equation into first one

`2v+v=24`

`3v=24`

`v=8`

now, we can plug this into second and third equation

`v=m+1`

we can plug it and find m

`8=m+1`

`m=7`

now, we can find e

`e+7=2* 8`

`e=9`

So, Emily's score was 9

(ii)

we got

e=9

m=7

9=7+2

e=m+2

Answer 2

Answer: Emily's score is 9; Equation (D) v = m+1

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.