1) Let s be the price of a senior citizen ticket and t be the price of a student ticket.
Equations:
4s + 5t = 102
7s + 5t = 126
Subtract the first equation from the second: (7s + 5t) - (4s + 5t) = 126 - 102 → 3s = 24 → s = 8.
Substitute s = 8 into the first equation: 4(8) + 5t = 102 → 32 + 5t = 102 → 5t = 70 → t = 14.
A senior citizen ticket costs $8 and a student ticket costs $14.
2) Let p be the speed of the plane in still air and w be the speed of the wind.
Equations:
p + w = 183
p - w = 141
Add the equations: (p + w) + (p - w) = 183 + 141 → 2p = 324 → p = 162.
Substitute p = 162 into the first equation: 162 + w = 183 → w = 21.
The plane's speed in still air is 162 km/h and the wind speed is 21 km/h.
3) Let a be the cost of an apple pie and m be the cost of a lemon meringue pie.
Equations:
6a + 4m = 80
6a + 5m = 94
Subtract the first equation from the second: (6a + 5m) - (6a + 4m) = 94 - 80 → m = 14.
Substitute m = 14 into the first equation: 6a + 4(14) = 80 → 6a + 56 = 80 → 6a = 24 → a = 4.
An apple pie costs $4 and a lemon meringue pie costs $14.
4) Let s be the price of a senior citizen ticket and c be the price of a child ticket.
Equations:
3s + 3c = 69
5s + 3c = 91
Subtract the first equation from the second: (5s + 3c) - (3s + 3c) = 91 - 69 → 2s = 22 → s = 11.
Substitute s = 11 into the first equation: 3(11) + 3c = 69 → 33 + 3c = 69 → 3c = 36 → c = 12.
A senior citizen ticket costs $11 and a child ticket costs $12.
5) Let c be the cost of a package of chocolate chip cookie dough and g be the cost of a package of gingerbread cookie dough.
Equations:
8c + 12g = 364
c + 4g = 93
Multiply the second equation by 8: 8c + 32g = 744.
Subtract the first equation from this: (8c + 32g) - (8c + 12g) = 744 - 364 → 20g = 380 → g = 19.
Substitute g = 19 into the second equation: c + 4(19) = 93 → c + 76 = 93 → c = 17.
A package of chocolate chip cookie dough costs $17 and a package of gingerbread cookie dough costs $19.
6) Let s be the price of a senior citizen ticket and c be the price of a child ticket.
Equations:
3s + 5c = 70
12s + 12c = 216
Simplify the second equation by dividing by 12: s + c = 18 → s = 18 - c.
Substitute into the first equation: 3(18 - c) + 5c = 70 → 54 - 3c + 5c = 70 → 2c = 16 → c = 8.
Then s = 18 - 8 = 10.
A senior citizen ticket costs $10 and a child ticket costs $8.
Parent Tip: Review the logic above to help your child master the concept of systems of equations word problems worksheet algebra 1.
