Answer:
Chloe is 5 years old
Explanation:
We will need a system of equations to find Chloe's age. We can allow C to represent Chloe's age and M to represent her mom's age.
First equation: Since we're told that Chloe is 29 years younger than her mom, the first equation we can use is C = M - 29
Second equation: Since we're also told that her mom's age is 1 less than 7 times Chloe's age, the second equation we can use is M = 7C - 1
Method to solve system: Substitution
We can use substitution to find Chloe's age.
Step 1: First, we need to isolate -29 in the first equation:
(C = M - 29) - M
C - M = -29
Step 2: Now we can substitute M = 7C - 1 for M in C - M = -29 to find C, Chloe's age:
C - (7C - 1) = -29
C - 7C + 1 = -29
-6C + 1 = -29
-6C = -30
C = 5
Thus, Chloe is 5 years old.
Optional Step 3: The only way we can check if our answer is correct is by finding the mom's age and seeing if it (along with Chloe's suspected age) satisfies both the verbal statements and the two equations in our systems themselves.
We can plug in 5 for C in the first equation to find M, the mom's age
5 = M - 29
34 = M
Checking first equation algebraically by plugging in 5 for C and 34 for M:
5 = 34 - 29
5 = 5
Checking first equation verbally: Chloe is indeed 29 years younger than her mom as her mom is 34, Chloe is 5, and 34 - 29 = 5
Checking second equation algebraically by plugging in 5 for C and 34 for M:
34 = 7(5) - 1
34 = 35 - 1
34 = 34
Checking first equation verbally: 7 times Chloe's age is 35 as 7 * 5 = 35 and 1 less than this is 34 as 35 - 1 = 34. Because the mom is 34, the numbers we've found for Chloe and the mom's age satisfies the verbal statement.