Let’s solve each problem step by step.
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Problem 1:
> Find the value of two numbers if their sum is 12 and their difference is 4.
Let the two numbers be
x and
y.
We write:
- x + y = 12 → (Equation 1)
- x - y = 4 → (Equation 2)
Add Equation 1 and Equation 2:
(x + y) + (x - y) = 12 + 4
→ 2x = 16
→ x = 8
Plug x = 8 into Equation 1:
8 + y = 12
→ y = 4
✔ Check: 8 + 4 = 12, 8 - 4 = 4 → Correct.
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Problem 2:
> The difference of two numbers is 3. Their sum is 13. Find the numbers.
Let the numbers be
x and
y.
We write:
- x - y = 3 → (Equation 1)
- x + y = 13 → (Equation 2)
Add them:
(x - y) + (x + y) = 3 + 13
→ 2x = 16
→ x = 8
Plug into Equation 2:
8 + y = 13
→ y = 5
✔ Check: 8 - 5 = 3, 8 + 5 = 13 → Correct.
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Problem 3:
> Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
Let:
- p = speed of plane in still air
- w = speed of wind
With tailwind: p + w = 158
Against wind: p - w = 112
Add the two equations:
(p + w) + (p - w) = 158 + 112
→ 2p = 270
→ p = 135
Now plug into first equation:
135 + w = 158
→ w = 23
✔ Check: 135 + 23 = 158, 135 - 23 = 112 → Correct.
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Problem 4:
> The school sold 3 senior citizen tickets and 1 child ticket for $38 on day 1. On day 2, they sold 3 senior and 2 child tickets for $52. Find price of senior and child ticket.
Let:
- s = price of senior ticket
- c = price of child ticket
Day 1: 3s + c = 38 → (Equation 1)
Day 2: 3s + 2c = 52 → (Equation 2)
Subtract Equation 1 from Equation 2:
(3s + 2c) - (3s + c) = 52 - 38
→ c = 14
Plug c = 14 into Equation 1:
3s + 14 = 38
→ 3s = 24
→ s = 8
✔ Check: Day 1: 3×8 + 14 = 24+14=38; Day 2: 3×8 + 2×14 = 24+28=52 → Correct.
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Final Answer:
1) 8 and 4
2) 8 and 5
3) Wind: 23 km/h, Plane: 135 km/h
4) Senior: $8, Child: $14
Parent Tip: Review the logic above to help your child master the concept of systems of equations word problems worksheet algebra 1.
