The sum of the ages of a brother and sister is 27. If four times the brother's age is subtracted from three times the sister's age, the difference is 11. Express your answer in terms of the symbols b and s. 27=?
To solve this problem, let's break it down into smaller steps:
Step 1: Define the variables:
Let's represent the brother's age as "b" and the sister's age as "s".
Step 2: Translate the given problem into equations:
We are given two conditions:
1. The sum of their ages is 27: b + s = 27
2. The difference between three times the sister's age and four times the brother's age is 11: 3s - 4b = 11
Step 3: Solve the equations:
To solve this system of equations, we can use any method such as substitution, elimination, or graphing. In this case, let's use the substitution method:
From equation 1 (b + s = 27), we can solve for b:
b = 27 - s
Now we substitute this value of b in equation 2 (3s - 4b = 11):
3s - 4(27 - s) = 11
3s - 108 + 4s = 11
7s - 108 = 11
7s = 119
s = 119/7
s = 17
Step 4: Find the value of b:
Now that we have the value of s, we can substitute it back into equation 1 to find b:
b + 17 = 27
b = 27 - 17
b = 10
Step 5: Express the answer in terms of symbols b and s:
The sum of their ages (27) can be expressed as:
b + s = 10 + 17 = 27
Therefore, the answer in terms of symbols b and s is:
27 = b + s = 10 + 17
Just translate the English into "Math"
"The sum of the ages of a brother and sister is 27" ---> b+s=27
" if four times the brother's age is subtracted from three times the sister's age, the difference is 11"
---> 3s - 4b = 11
Solve
(I assume you know how to solve these two equations.)