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goldenfox [79]
3 years ago
10

Tuli is 10 years younger than Emily. The product of their

Mathematics
1 answer:
Naya [18.7K]3 years ago
3 0

Answer:

a² - 14a - 15 = 0 (quadratic equation)

Emily's age = 15 years

Tuli's age = 15 - 10 = 5 years

Step-by-step explanation:

let

Emily age = a

Tuli age =  a - 10

Two years ago their ages will be as follows.

Emily's age = a - 2

Tuli's age = a - 10 - 2 = a - 12

The product of their ages 2 years ago is 39.

(a - 2)(a - 12) = 39

a² - 12a - 2a + 24 - 39 = 0

a² - 14a - 15 = 0 (quadratic equation)

To get a

a² + a - 15a - 15 = 0

a(a + 1) - 15(a + 1)

(a + 1)(a - 15)

a = -1 or 15

we can only use 15 as it is positive.

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Okay so to represent juice we are going to use X, and to represent water we are going to use Y.

We also know that the first two starting equations are:

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Now you can take that equation and plug into either one of the starting two equations.  I chose the second equation.  We just substitute what y equals in for y in the equation, so we have:

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y = 135 - 6(20)

y = 135 - 120

y = 15

The price of water costs $15

From this we can conclude that the cost of juice is $20 and the price of water is $15

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