Question

How to solve this equation a + b = 40 and 5.50a + 3b = 4(40)?

A) a = 10, b = 30
B) a = 30, b = 10
C) a = 20, b = 20
D) a = 40, b = 0

Answer 1

To solve the given system of equations, one can start by solving the first equation for a, then substitute this expression into the second equation to find b. After obtaining b, plug this value back into the first equation to find a. The solution found, a = 16 and b = 24, is not present in the given options.

Step-by-step explanation:

To solve the system of equations a + b = 40 and 5.50a + 3b = 4(40), we can use the substitution or elimination method. Let us start with the first equation.

1. Write down the given equations:

• Equation 1: a + b = 40
• Equation 2: 5.50a + 3b = 160 (since 4 times 40 is 160)

Solve Equation 1 for a:

• a = 40 - b

Substitute the expression for a from step 2 into Equation 2:

• 5.50(40 - b) + 3b = 160

Simplify and solve for b:

• 220 - 5.50b + 3b = 160
• -2.50b = -60
• b = 24

Substitute b into Equation 1 to find a:

• a + 24 = 40
• a = 16

Thus, the solution is a = 16 and b = 24, which is not among the given options.