The miller family made a mathematical statements out of their ages as follows. tom is four less than twice gary’s age. rebecca is the youngest and she is two less than half gary’s age after it was increased by three. sam’s age is the ratio of seven more than gary’s age to eight less than gary’s age. translate each of the miller family members ages into algebraic expressions in terms of gary’s age, g.

Let us assume Gary's age = g years.

Tom is four less than twice of Gary's age.

We took g for Gary's age, therefore "4 less than twice of g would be" 2g-4.

Therefore, Tom's age = 2g-4.

Rebecca is two less than half Gary’s age after it was increased by three.

After increasing g by 3, we get g+3.

Half of (g+3) = 1/2 (g+3).

Now 2 less than half after it was increased by three = 1/2(g+3)-2.

Therefore, Rebecca's age = 1/2(g+3)-2.

Sam's age = 7 more than Gary's age : 78 less than Gary's age.

Therefore, Sam's age = (g+7)/(g-8).

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