Answer:
-1 and -2, or 9 and 10
Step-by-step explanation:
If x is the smaller integer:
x (x + 1) = 14 + 4 (x + x + 1)
x² + x = 14 + 4 (2x + 1)
x² + x = 14 + 8x + 4
x² − 7x − 18 = 0
Factor using AC method:
(x − 9) (x + 2) = 0
x = -2 or 9
x is the smaller integer, so the larger integers are -1 and 10. Check each pair of solutions.
-1 and -2:
(-2) (-1) = 14 + 4 (-2 + -1)
2 = 14 + 4 (-3)
2 = 2
9 and 10:
(9) (10) = 14 + 4 (9 + 10)
90 = 14 + 4 (19)
90 = 90
Both solutions work.
Answer:
-4 + 9
9- 4
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer: 74 adult tickets were sold on Wednesday.
Step-by-step explanation:
Let x represent the number of child admission tickets sold on Wednesday.
Let y represent the number of adult admission tickets sold on Wednesday.
On Wednesday, 128 tickets were sold. It means that
x + y = 128
At the movie theatre, child admission is $6.40 and adult admission is $9.70. The total ticket sales on Wednesday was $1063.40. It means that
6.4x + 9.7y = 1063.4- - - - - - - - - - 1
Substituting x = 128 - y into equation 1, it becomes
6.4(128 - y) + 9.7y = 1063.4
819.2 - 6.4y + 9.7y = 1063.4
- 6.4y + 9.7y = 1063.4 - 819.2
3.3y = 244.2
y = 244.2/3.3
y = 74
x = 128 - y = 128 - 74
x = 54
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