anita, cheri, miguel, and jake went bowling one night for fun they decided to pit the girls against the boys, with the highest score for each team winning.

anita scored 18 less than miguel, cheri's score was 16 less than twice anita's, cheri outscored jake by 21.

if the total score by all four kids was 529, what was the final scores of the match?

M (Miguel) = M
A (Anita) = M - 18
C (Cheri)= 2(M - 18) - 16
J (Jake) = [2(M - 18) - 16] -21
529 = M+(M-18)+[2(M-18)-16]+[2(M-18)-16-21]
529 = 6M + 143
M = 112
A = 94
C = 172
J = 151

where does the 143 come from???

I believe that the 143 is a mistake. It should be -127.

To solve this problem, let's assign variables to each person's score:

M represents Miguel's score.
A represents Anita's score.
C represents Cheri's score.
J represents Jake's score.

Based on the given information, we can establish the following equations:

Anita scored 18 less than Miguel: A = M - 18
Cheri's score was 16 less than twice Anita's: C = 2(A) - 16
Cheri outscored Jake by 21: C = J + 21

We also know that the total score of all four kids is 529:

M + A + C + J = 529

Using the equations above, we can substitute and solve for the variables.

First, we substitute A in terms of M in the equation for C:

C = 2(A) - 16
C = 2(M - 18) - 16
C = 2M - 36 - 16
C = 2M - 52

Next, we substitute C in terms of J in the equation:

C = J + 21
2M - 52 = J + 21
J = 2M - 73

Now, we substitute the values of A, C, and J in terms of M into the equation for the total score:

M + A + C + J = 529
M + (M - 18) + (2M - 52) + (2M - 73) = 529
6M - 143 = 529
6M = 672
M = 112

Now that we have Miguel's score (M = 112), we can substitute it back into the equations to find the other scores:

A = M - 18
A = 112 - 18
A = 94

C = 2M - 52
C = 2(112) - 52
C = 224 - 52
C = 172

J = 2M - 73
J = 2(112) - 73
J = 224 - 73
J = 151

Therefore, the final scores of the match are:
Miguel: 112
Anita: 94
Cheri: 172
Jake: 151