Assume that y varies directly with x. If y=9 when x=−3, find x when y=6. Enter in any fractions using a / (e.g. "1/2" is the sam
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Answer:
Here, K represents the current age of Katie and T represents the current age of Thomas.
(a)
As per the statement:
Katie is currently twice the age of Thomas.
⇒ ......[1]
It is also given that in 6 years Katie will be 4 times Thomas's current age.
Subtract 6 from both sides we get;
......[2]
A system of equations that describe the situation is:
(b)
To find the solution:
equate [1] and [2] we have;
Subtract 2T from both sides we have;
Add 6 to both sides we get;
Divide both sides by 2 we have;
T = 3 years
Substitute this in equation [1] we get;
K = 2(3) = 6 years.
Therefore, the current age of Katie and Thomas are 6 years and 3 years.