the difference between two numbers is 55. four times the smaller number plus 5 times the larger number is 176. what are the numbers?
L-S=55
4S+5L=176
solve by substution.
To solve this problem, we will use the substitution method. Here's how you can do it step by step:
1. Start by solving the first equation for one variable (let's solve for L):
L - S = 55
L = S + 55
2. Substitute the expression for L in the second equation:
4S + 5L = 176
4S + 5(S + 55) = 176
3. Simplify the equation:
4S + 5S + 275 = 176
9S + 275 = 176
4. Move the constant term (275) to the other side of the equation by subtracting it from both sides:
9S = 176 - 275
9S = -99
5. Divide both sides of the equation by 9 to isolate S:
S = -99 / 9
S = -11
6. Now that we have the value for S, substitute it back into the expression we found for L:
L = S + 55
L = -11 + 55
L = 44
Therefore, the two numbers are -11 and 44. The smaller number is -11, and the larger number is 44.