The ratio of boys to girls at a day care center is 5 to 4. Which of following cannot be the total number of children at the center?
A. 27
B. 54
C. 60
D. 72
5x + 4x = 27, 54, 60, 72
Solve for x for each number. Which every does not solve as a whole number is the answer.
I'm not understanding. Please show me how to solve.
With a ratio of 5:4, the total needs to be some multiple of 9. Which is not a multiple of 9?
72
But how should it be 72 if 72 is a multiple of 9. 9 x 8 =72
60
To determine which option cannot be the total number of children at the center, we need to find a ratio of boys to girls that cannot be satisfied with the given options.
The ratio of boys to girls is 5 to 4. This means that for every 5 boys, there are 4 girls.
Now let's check each option:
A. 27: If there are 27 children, we can divide them into groups of 5 boys and 4 girls (since 27 can be divided evenly by 9, which is the total number of parts in the ratio 5:4). Therefore, A is a possible answer.
B. 54: If there are 54 children, we can divide them into groups of 30 boys and 24 girls (since 54 can be divided evenly by 9 and multiplied by 5 and 4, respectively). Therefore, B is a possible answer.
C. 60: If there are 60 children, we can divide them into groups of 35 boys and 28 girls (since 60 can be divided evenly by 9 and multiplied by 5 and 4, respectively). Therefore, C is a possible answer.
D. 72: If there are 72 children, we can divide them into groups of 40 boys and 32 girls (since 72 can be divided evenly by 9 and multiplied by 5 and 4, respectively). Therefore, D is a possible answer.
Since all the options can be satisfied with the given ratio, none of the options cannot be the total number of children at the center.