Answer:
Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30
When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution
When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions
Step-by-step explanation:
* Lets read the problem and solve it
- There are three sisters ⇒ Maggie , Karen , Jasmine
- Each sister bought a gift for their mom
- Maggie spent 3 times as much as Karen
- Karen spent half as much as Jasmine
- Altogether, they spent $60
- Let Jasmine spent x
∵ Karen spent half as much as Jasmine
∴ Karen spent 1/2 x
∵ Maggie spent 3 times as much as Karen
∴ Maggie spent 3 × 1/2 x = 3/2 x
∵ Altogether, they spent $60
∴ x + 1/2 x + 3/2 x = 60
∴ 3x = 60 ⇒ divide both sides by 3
∴ x = 20
* Lets find the share of each one
∵ Jasmine spent x
∴ Jasmine spent $20
∵ Karen spent 1/2 x
∴ Karen spent 1/2 × 20 = $10
∵ Maggie spent 3/2 x
∴ Maggie spent 3/2 x 20 = $30
* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30
* Lets describe what happens when an equation has no solution
- "No solution" means that there are no values of x satisfy the equation
- When x disappears from the equation and the two sides of the
equation not equal each other , then the equation has no solution
- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x
∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms
∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides
∴ 4 = 5 ⇒ the two sides not equal
∴ There is no value of x satisfy this equation
∴ There is no solution
* Lets describe what happens when an equation has infinite solutions
- "Infinite solutions" means all numbers are solutions.
- When x disappears from the equation and the two sides of the
equation equal each other , then the equation has infinite solutions
- Ex: solve the equation 2x + 3 = x + x + 3
∵ 2x + 3 = x + x + 3 ⇒ add the like terms
∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides
∴ 3 = 3 ⇒ the two sides are equal
∴ All values of x satisfy the equation
∴ There are infinite solutions
