Answer:
Model (2) has the same number of days as Mika
Step-by-step explanation:
- The relationship models are:
→ y = -2x - 12 ⇒ (1)
→ y = -3x + 18 ⇒ (2)
→ y = -4x + 12 ⇒ (3)
→ y = -12x + 2 ⇒ (4)
- We need to find the relationship model that will reach $0 in the
same number of days as this scenario:
Mika has $12 and spends $2 each day
- The rate of spends of Mika is $2 per day
∵ x is the number of days
∵ y is the amount of money after x days
∵ Mika has $12
∵ Mika spends $2 each day
∴ y = -2x + 12
- We need to know the amount of money will be $0 after how
many days
- Put y = 0
∴ 0 = -2x + 12
- Subtract 12 from both sides
∴ -12 = -2x
- Divide both sides by -2
∴ x = 6
∴ Mika will have $0 after 6 days
- Let us do the same in each model to find x and then find which of
them have the same x as Mika
→ Model (1)
∵ 0 = -2x - 12
- Add 12 to both sides
∴ 12 = -2x
-Divide both sides by -2
∴ x = -6
→ Model (2)
∵ 0 = -3x + 18
- Subtract 18 from both sides
∴ -18 = -3x
-Divide both sides by -3
∴ x = 6
→ Model (3)
∵ 0 = -4x + 12
- Subtract 12 from both sides
∴ -12 = -4x
-Divide both sides by -4
∴ x = 3
→ Model (4)
∵ 0 = -12x + 2
- Subtract 2 from both sides
∴ -2 = -12x
-Divide both sides by -12
∴ x = 1/6
* Model (2) has the same number of days as Mika
