**3. Set up the equation. You know that they ate 44 hotdogs together.**
Urban’s hotdogs + Olivia’s hotdogs + Viktor’s hotdogs = 44 hotdogs
*x* + 3 + *x* + *x* – 4 = 44
4. Solve the equation
*x* + 3 + *x* + *x* – 4 = 44
3*x* - 1 = 44
3*x* = 45
*x* = 15
**5. Check that the solution is correct **
The equation: *x* + 3 + *x* + *x* – 4 = 44
Check with *x* = 15;
15 + 3 + 15 + 15 – 4 = 44
LHS = RHS, it is correct.
We now go back to the different expressions and replace *x* with 15.
Olivia = *x* hotdogs = 15 hotdogs
Urban = *x* hotdogs + 3 hotdogs = 15 + 3 = 18 hotdogs
Viktor = *x* hotdogs – 4 hotdogs = 15 – 4 = 11 hotdogs
**6. Write the answer**
Answer: Olivia ate 15 hotdogs, Urban ate 18 hotdogs and Viktor ate 11 hotdogs.
Urban then won the hotdog eating contest.
**Problem Solving by using Figures and Equations**
A very good way to simplify equation solving is to use figures.
Example:
Tyra cycles twice as far as Linnea and Dejan cycles 5 km farther than Linnea. In total they cycle 45 km together. How far do they each cycle?
Draw a figure and then it becomes much easier to write an equation.
We assume that Linnea cycles *x *km
Tyra cycles: 2*x *km
Dejan cycles r: *x* + 5 km
Together they have cycled 45 km.
We set up an equation: *x* + 2*x* + *x* + 5 = 45
Solve the equation:
*x* + 2*x* + *x* + 5 = 40
4*x* = 40
*x* = 10
We check that it is correct:
10 + 2 **·** 10 + 10 + 5 = 45
It is correct!
Answer:
Linnea cycles: 10 km
Tyra cycles: 2 **·** 10 = 20 km
Dejan cycles: 10 + 5 = 15 km |