SOLUTION
Given B is the midpoint of AC ABBC 1 and C is the midpoint of BD BCCD2 ie on adding 1 and 2 ART We get ABBCBCCD hence ABCD hence proved
hi,
Express the ratios in fractional form, that is
= ( cross- multiply )
y + 3 = k(y + 5) ← distribute
y + 3 = ky + 5k ( subtract ky from both sides )
y - ky + 3 = 5k ( subtract 3 from both sides )
y - ky = 5k - 3 ← factor out y from each term on the left side
y(1 - k) = 5k - 3 ← divide both sides by (1 - k)
y = 5k- 3
____
1 - k
Answer: 321 adult tickets and 227 children tickets were sold.
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of children tickets that were sold.
The total number of tickets that the theatre sold is 548. This means that
x + y = 548
Adult tickets sell for $6.50 each, and children's tickets sell for $3.50 each. The total ticket sales was $2881. This means that
6.5x + 3.5y = 2881 - - - - - - - - - - -1
Substituting x = 548 - y into equation 1, it becomes
6.5(548 - y) + 3.5y = 2881
3562 - 6.5y + 3.5y = 2881
- 6.5y + 3.5y = 2881 - 3562
- 3y = - 681
y = - 681/ -3
y = 227
x = 548 - y = 548 - 227
x = 321
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