1. Let A be the number of adult tickets and C be the number of child tickets.
Equations: A + C = 8 and 11A + 7C = 76.
Solving gives A = 5, C = 3. So, 5 adult tickets and 3 child tickets were purchased.
2. Let x be the number.
Equation: 5x - 28 = 232.
Solving gives x = 52.
3. Let the integers be x, x+2, x+4.
Equation: x + (x+2) + (x+4) = 123.
Solving gives x = 39, so the integers are 39, 41, 43. However, these are not even. There is no solution with three consecutive even integers summing to 123.
4. Let the numbers be x, x+2, x+4.
Equation: x + (x+2) + (x+4) = 276.
Solving gives x = 90, so the numbers are 90, 92, 94.
5. Let the first angle be x degrees.
Then the second angle is 2x, and the third is x - 40.
Equation: x + 2x + (x - 40) = 180.
Solving gives x = 55, so the angles are 55°, 110°, and 15°.
Parent Tip: Review the logic above to help your child master the concept of creating linear equations from word problems worksheet.
