Six years ago Matt was four times as old as Brown, and in 3 years the sum of their ages will be 43 years. Find their present ages.
To solve this problem, let's assign variables to represent the current ages of Matt and Brown. Let's assume Matt's current age is M, and Brown's current age is B.
According to the given information, six years ago, Matt was four times as old as Brown. This can be expressed as:
M - 6 = 4(B - 6) ---(1)
In 3 years, the sum of their ages will be 43 years. This can be expressed as:
(M + 3) + (B + 3) = 43 ---(2)
Now, let's solve these two equations to find the present ages of Matt and Brown.
Expanding equation (1), we get:
M - 6 = 4B - 24
Rearranging the terms, we have:
M = 4B - 24 + 6
M = 4B - 18 ---(3)
Substituting equation (3) into equation (2), we get:
(4B - 18 + 3) + (B + 3) = 43
Simplifying, we have:
5B - 15 = 43
Adding 15 to both sides of the equation, we get:
5B = 58
Dividing both sides of the equation by 5, we get:
B = 11.6
Since Brown's age cannot be a decimal, we will consider the nearest whole number, which is 12.
Substituting B = 12 into equation (3), we have:
M = 4(12) - 18
M = 48 - 18
M = 30
Therefore, currently Matt is 30 years old and Brown is 12 years old.
To solve this problem, let's assign variables to represent Matt's and Brown's ages.
Let's say Matt's current age is M, and Brown's current age is B.
From the information given, we can set up two equations:
1) "Six years ago, Matt was four times as old as Brown":
M - 6 = 4(B - 6)
2) "In 3 years, the sum of their ages will be 43 years":
(M + 3) + (B + 3) = 43
Now, let's solve these equations to find the values of M and B.
1) Expanding the equation (using the distributive property):
M - 6 = 4B - 24
Simplifying:
M = 4B - 18
2) Substituting this value of M into the second equation:
(4B - 18 + 3) + (B + 3) = 43
Simplifying:
5B - 12 = 43
5B = 55
B = 11
Now that we know Brown's age, we can substitute this value back into the first equation to find Matt's age:
M = 4B - 18
M = 4(11) - 18
M = 44 - 18
M = 26
Therefore, Matt's present age is 26 and Brown's present age is 11.
Six years ago ....
Brown' age ==== x
Matt's age ==== 4x
in 3 years:
Brown = x+9
Matt = 4x + 9
4x+9 + x+9 = 43
solve for x, then find x+4 and 4x+4