Answer:
x + 10 = 4x
Step-by-step explanation:
Let x = her age 10 years ago.
Her age now is x + 10.
x + 10 = 4x
We know the total tickets sold = 400.
Let x be the number of adult tickets sold.
That means 400 - x is the number of student tickets.
The revenue from adult tickets will be $3 * x, which we can call 3x.
The revenue from student ticks will be $2 * (400 - x), or 800 - 2x.
The total revenue is $1050, so that means:
3x + (800 - 2x) = 1050.
Removing the parentheses:
3x + 800 - 2x = 1050
Subtracting 800 from both sides:
3x - 2x = 250
Simplifying the left side:
x = 250, which is the number of adult tickets.
400-x = student tickets = 400-250 = 150.
ALWAYS check!
In this case, check the revenue:
3x = 3(250) = 750
2(150) = 300
750 + 300 = 1050. Check!
<span>3x + y = 9 (I)
</span><span>y = –4x + 10 (II)
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![\left \{ {{3x + y = 9 } \atop {y = -4x + 10 }} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7B3x%20%2B%20y%20%3D%209%20%7D%20%5Catop%20%7By%20%3D%20-4x%20%2B%2010%20%7D%7D%20%5Cright.%20)
Pass the incognito "4x" to the first term, changing the signal when changing sides.
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simplify by (-1)
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![\left \{ {{3x + y = 9.(-1)} \atop {4x + y = 10 }} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B3x%20%2B%20y%20%3D%209.%28-1%29%7D%20%5Catop%20%7B4x%20%2B%20y%20%3D%2010%20%7D%7D%20%5Cright.%20)
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![\left \{ {{- 3x - \diagup\!\!\!\!y =-9} \atop {4x + \diagup\!\!\!\!y = 10}} \right. ](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7B-%203x%20-%20%5Cdiagup%5C%21%5C%21%5C%21%5C%21y%20%3D-9%7D%20%5Catop%20%7B4x%20%2B%20%5Cdiagup%5C%21%5C%21%5C%21%5C%21y%20%3D%2010%7D%7D%20%5Cright.%20%20%20%20%20%0A%20)
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![\left \{ {{- 3x = - 9} \atop {4x = 10}} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7B-%203x%20%3D%20-%209%7D%20%5Catop%20%7B4x%20%3D%2010%7D%7D%20%5Cright.%20)
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![\boxed{x = 1}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%20%3D%201%7D)
<span><span>
</span></span><span>Substitute in equation (I) to find the value of "Y".
</span>3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3
![\boxed{y = 6}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%206%7D)
Answer:
![\boxed{\boxed{ \left \ {{x=1} \atop {y=6}} \right. }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5Cleft%20%5C%20%7B%7Bx%3D1%7D%20%5Catop%20%7By%3D6%7D%7D%20%5Cright.%20%7D%7D)