Is y=0.5x + 2 a linear function
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1. Dorothy paid $200 for the teddy bear
2. y is more than x by %
Step-by-step explanation:
1. The given is:
- Dorothy bought a teddy bear and sold it at a 20% profit to Kim
- Kim bought a suit costing $100 and dressed the teddy bear up in the suit
- Kim then sold the teddy bear in the suit to Karen for $442
- Kim made a profit of 30%
We need to find how much Dorothy paid for the teddy bear
Assume that Dorothy bought a teddy bear for $x
∵ Dorothy bought a teddy bear for $x
∵ She sold it at a profit 20% to Kim
By using the ratio method
→ Buying price : Profit : Selling price
→ 100% : 20% : 120% ⇒ (100% + 20%)
→ x : : ?
By using cross multiplication
∴ 100% × Selling price = x × 120%
- Divide both sides by 100%
∴ Selling price = 1.2x
∴ Dorothy sold the teddy bear for $1.2x to Kim
∵ Kim bought a suit costing $100 and dressed the teddy bear
up in the suit
∴ The cost of the teddy bear = 1.2x + 100
∵ Kim sold the teddy bear in the suit to Karen for $442
∵ Kim made a profit of 30%
By using the ratio method
→ Cost price : Profit : Selling price
→ 100% : 30% : 130% ⇒ (100% + 30%)
→ 1.2x + 100 : : 442
By using cross multiplication
∴ (1.2x + 100) × 130% = 100% × 422
- Divide both sides by 130%
∴ 1.2x + 100 = 340
- Subtract 100 from both sides
∴ 1.2x = 240
- Divide both sides by 1.2
∴ x = 200
∴ Dorothy bought the teddy bear for $200
Dorothy paid $200 for the teddy bear
2. The given is:
- x is less than y by 25%
- Then y is more than x by how many percent
Assume that y is 100%
∵ y = 100%
∵ x is less than y by 25%
∴ x = 100% - 25%
∴ x = 75%
- The percentage of increasing of y = × 100%
∵ The percentage of increasing of y = × 100%
∴ The percentage of increasing of y = × 100%
∴ The percentage of increasing of y = × 100%
∴ The percentage of increasing of y = %
y is more than x by %
Learn more:
You can learn more about the ratio in brainly.com/question/4713715
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