Sure, let's solve the problem step by step.
1. Understand the relationships given in the problem:
- 8% of the number of oranges is equal to 20% of the number of watermelons.
- There are 180 more oranges than watermelons.
2. Assign variables:
Let [tex]\( w \)[/tex] be the number of watermelons.
Let [tex]\( o \)[/tex] be the number of oranges.
3. Translate the relationships into equations:
From the first relationship:
[tex]\( 0.08 \times \text{number of oranges} = 0.2 \times \text{number of watermelons} \)[/tex]
In variables, this becomes:
[tex]\( 0.08 \times o = 0.2 \times w \)[/tex]
From the second relationship:
[tex]\( o = w + 180 \)[/tex]
4. Substitute the second equation into the first:
Substitute [tex]\( o = w + 180 \)[/tex] into [tex]\( 0.08 \times o = 0.2 \times w \)[/tex]:
[tex]\( 0.08 \times (w + 180) = 0.2 \times w \)[/tex]
5. Solve for [tex]\( w \)[/tex]:
Distribute the 0.08:
[tex]\( 0.08w + 14.4 = 0.2w \)[/tex]
Move all terms involving [tex]\( w \)[/tex] to one side:
[tex]\( 14.4 = 0.2w - 0.08w \)[/tex]
Simplify:
[tex]\( 14.4 = 0.12w \)[/tex]
Solve for [tex]\( w \)[/tex]:
[tex]\( w = \frac{14.4}{0.12} \)[/tex]
[tex]\( w = 120 \)[/tex]
Thus, the number of watermelons is 120.
