Bret is presently 9 years older than Juan. In 8 years, 6 times Bret's age will equal 7 times Juan's age. What are Bret's and Juan's present ages?
b = j+9
6(b+8) = 7(j+8)
now just solve for b and j.
To solve this problem, let's start by translating the given information into equations.
Let's assume Bret's present age is B and Juan's present age is J.
According to the problem, Bret is presently 9 years older than Juan, so we can write the equation:
B = J + 9 -- equation (1)
In 8 years, 6 times Bret's age will equal 7 times Juan's age, so we can write the equation:
6(B + 8) = 7(J + 8) -- equation (2)
Now we have a system of two equations (equations 1 and 2) with two variables (B and J). We can solve this system of equations to find the values of B and J.
First, let's simplify equation (2):
6B + 48 = 7J + 56
Next, let's substitute the value of B from equation (1) into equation (2):
6(J + 9) + 48 = 7J + 56
6J + 54 + 48 = 7J + 56
6J + 102 = 7J + 56
Now, let's isolate the variable terms on one side and the constant terms on the other side:
6J - 7J = 56 - 102
-J = -46
Finally, let's solve for J by multiplying both sides by -1:
J = 46
Now that we know Juan's present age (J = 46), we can substitute this value back into equation (1) to find Bret's present age:
B = J + 9
B = 46 + 9
B = 55
Therefore, Juan's present age is 46 years and Bret's present age is 55 years.