Lina is now 5 times as old as Bob, but 7 years from now, she will be 3 times as old as he will be then. How old is Lina now?
well, if their ages now are x and y, then their ages in 7 years will be x+7 and y+7.
Now just write your equations and solve them.
Y= 5x+7
Lina is 35 years old.
To solve this problem, let's first assign variables to represent Lina's and Bob's current ages. Let's call Lina's age "L" and Bob's age "B".
According to the problem, we know that Lina is now 5 times as old as Bob, so we can write the equation:
L = 5B ---(Equation 1)
We are also given that 7 years from now, Lina will be 3 times as old as Bob will be then. That means we need to add 7 to their respective ages and set up another equation:
L + 7 = 3(B + 7) ---(Equation 2)
Now we have a system of two equations with two variables (L and B). We can solve this system to find the values.
To do that, we can use the substitution method or the elimination method. In this case, let's solve it using the substitution method.
Step 1: Rearrange Equation 1 to solve for L:
L = 5B
Step 2: Substitute Equation 1 into Equation 2:
5B + 7 = 3(B + 7)
Step 3: Distribute the 3 on the right side:
5B + 7 = 3B + 21
Step 4: Subtract 3B from both sides:
5B - 3B + 7 = 21
Step 5: Simplify:
2B + 7 = 21
Step 6: Subtract 7 from both sides:
2B + 7 - 7 = 21 - 7
Step 7: Simplify:
2B = 14
Step 8: Divide both sides by 2:
2B/2 = 14/2
Step 9: Simplify:
B = 7
Now that we know Bob's age is 7, we can substitute this value into Equation 1 to find Lina's age:
L = 5B
L = 5(7)
L = 35
So, Lina is currently 35 years old.