Question

Ava’s turtle is half as old as her parent. In 10 years, her total will be 3/4 as old as her parent. Write an equation to represent the situation. How old is Ava’s turtle?

A. Let t represent the turtle's current age and p represent the parent's current age. The equation is t = (1/2)p, and in 10 years, t + 10 = (3/4)(p + 10).
B. Let t represent the turtle's current age and p represent the parent's current age. The equation is t = 2p, and in 10 years, t + 10 = (3/4)(p + 10).
C. Let t represent the turtle's current age and p represent the parent's current age. The equation is t = (1/4)p, and in 10 years, t + 10 = (3/4)(p + 10).
D. Let t represent the turtle's current age and p represent the parent's current age. The equation is t = (3/4)p, and in 10 years, t + 10 = (1/2)(p + 10).

Answer 1

Ava's turtle is half as old as her parent, leading to the equation t = 1/2p. In 10 years, the turtle will be 3/4 as old as her parent, leading to the equation t + 10 = 3/4(p + 10). Option A is correct and we can solve for t using these equations.

Step-by-step explanation:

To find the age of Ava's turtle, we can write two equations based on the information given. Initially, Ava's turtle is half as old as her parent, which gives us the first equation t = \(\frac{1}{2}p\), with t representing the turtle's current age and p representing the parent's current age. After 10 years, Ava's turtle will be 3/4 as old as her parent, leading to the second equation t + 10 = \(\frac{3}{4}\)(p + 10). If we look at the options:
A is correct: t = \(\frac{1}{2}p\) and t + 10 = \(\frac{3}{4}\)(p + 10),
B is incorrect as it suggests t = 2p which is not 'half as old',
C is incorrect as it suggests t = \(\frac{1}{4}p\) which does not align with being 'half as old',
D is incorrect as it suggests a wrong relationship in both parts of the question.
The correct answer is A, and to solve for t, we can use substitution or another method of solving simultaneous equations.