1. Let $a$ be the number of adult tickets and $c$ be the number of child tickets.
Equations:
$a + c = 8$
$11a + 7c = 76$
Solving: From the first equation, $c = 8 - a$. Substitute into the second:
$11a + 7(8 - a) = 76$
$11a + 56 - 7a = 76$
$4a = 20$
$a = 5$
Then $c = 8 - 5 = 3$.
Answer: 5 adult tickets and 3 child tickets.
2. Let the number be $x$.
Equation: $5x - 28 = 232$
$5x = 260$
$x = 52$
Answer: 52
3. Let the three consecutive even integers be $x$, $x+2$, $x+4$.
Equation: $x + (x+2) + (x+4) = 123$
$3x + 6 = 123$
$3x = 117$
$x = 39$
But 39 is odd, so no solution exists for consecutive *even* integers summing to 123.
Answer: No solution (sum of three consecutive even integers must be even; 123 is odd).
4. Let the three consecutive even numbers be $x$, $x+2$, $x+4$.
Equation: $x + (x+2) + (x+4) = 276$
$3x + 6 = 276$
$3x = 270$
$x = 90$
The numbers are 90, 92, 94.
Answer: 90, 92, 94
5. Let the first angle be $x$ degrees.
Second angle: $2x$
Third angle: $x - 40$
Sum of angles in a triangle is 180°:
$x + 2x + (x - 40) = 180$
$4x - 40 = 180$
$4x = 220$
$x = 55$
Angles: 55°, 110°, 15°.
Answer: 55°, 110°, 15°
Parent Tip: Review the logic above to help your child master the concept of two variable word problems worksheet.
