Solve: [tex]3 b c+4 a+6 c[/tex] when [tex]a=4, b=6, c=8[/tex]
Answer (1)
Substitute the given values a = 4 , b = 6 , and c = 8 into the expression 3 b c + 4 a + 6 c .
Calculate the product 3 ( 6 ) ( 8 ) = 144 .
Calculate the product 4 ( 4 ) = 16 and 6 ( 8 ) = 48 .
Add the results: 144 + 16 + 48 = 208 . The final answer is 208 .
Explanation
Understanding the Problem We are given the expression 3 b c + 4 a + 6 c and the values a = 4 , b = 6 , and c = 8 . Our goal is to substitute these values into the expression and simplify to find the final answer.
Substituting the Values First, we substitute the given values into the expression: 3 b c + 4 a + 6 c = 3 ( 6 ) ( 8 ) + 4 ( 4 ) + 6 ( 8 )
Performing the Multiplications Next, we perform the multiplications: 3 ( 6 ) ( 8 ) = 18 ( 8 ) = 144 4 ( 4 ) = 16 6 ( 8 ) = 48
Adding the Results Now, we add the results: 144 + 16 + 48 = 160 + 48 = 208
Final Answer Therefore, the value of the expression 3 b c + 4 a + 6 c when a = 4 , b = 6 , and c = 8 is 208 .
Examples
Imagine you are calculating the total cost of materials for a project. You need 3 pieces of material 'b' which costs 6 dollars each and each piece is 8 units long, 4 pieces of material 'a' which costs 4 dollars each, and 6 pieces of material 'c' which costs 8 dollars each. The expression 3 b c + 4 a + 6 c helps you calculate the total cost: 3 ( 6 ) ( 8 ) + 4 ( 4 ) + 6 ( 8 ) = 144 + 16 + 48 = 208 dollars. This kind of calculation is useful in budgeting and resource management.
