Jill's age 5 years ago was 4 less than 3 times barry's current age. if the product of their ages now is 200, what is each of their current ages?
J = 200/B
J-5 = 3B - 4
Substitute 200/B for J in the second equation and solve for B. Insert that value into the first equation to solve for J. Check by putting both values into the second equation.
To find Jill's and Barry's current ages, let's solve this step by step:
Let's assume that Jill's current age is J and Barry's current age is B.
According to the given information:
1. Jill's age 5 years ago was 4 less than 3 times Barry's current age:
J - 5 = 3B - 4
2. The product of their ages now is 200:
J * B = 200
Now, we have a system of equations to solve:
Equation 1: J - 5 = 3B - 4
Equation 2: J * B = 200
To solve for J and B, we can use the substitution method.
Step 1: Rearrange Equation 1 to express J in terms of B:
J = 3B - 4 + 5
J = 3B + 1
Step 2: Substitute the expression for J in Equation 2:
(3B + 1) * B = 200
3B^2 + B - 200 = 0
Step 3: Now, we solve the quadratic equation. There are different methods available, such as factoring, completing the square, or using the quadratic formula. Let's use factoring:
(3B + 25)(B - 8) = 0
Setting each factor to zero:
3B + 25 = 0 or B - 8 = 0
B = -25/3 or B = 8
Since ages cannot be negative, we discard B = -25/3.
Thus, Barry's current age is B = 8.
Step 4: Substitute B = 8 back into Equation 1 to find Jill's current age:
J = 3(8) + 1
J = 24 + 1
J = 25
Hence, Jill's current age is J = 25 and Barry's current age is B = 8.