Flippin' heck! (Clapping)(Clapping)(Clapping)MarkFL said:Hello anemone! (Sun)
My solution:
If we multiply the first equation by 18, and the rest by 13, and then add them together, we obtain:
\(\displaystyle 135a+140b+145c+150d=9500\)
Dividing through by 5, we then get:
\(\displaystyle 27a+28b+29c+30d=1900\)
MarkFL said:Hello anemone! (Sun)
My solution:
If we multiply the first equation by 18, and the rest by 13, and then add them together, we obtain:
\(\displaystyle 135a+140b+145c+150d=9500\)
Dividing through by 5, we then get:
\(\displaystyle 27a+28b+29c+30d=1900\)
anemone said:...your solution is smarter and neater than mine! Bravo, Mark!...
anemone has mentioned 27a+28b+29c+30d=30(a+b+c+d)−(3a+2b+c).anemone said:Hello MarkFL!(Sun)
Thanks for participating and hey, your solution is smarter and neater than mine! Bravo, Mark!
My solution:
Adding those four equations yields
$10(a + b + c + d) = 630$ and this gives $a + b + c + d=63$.
But we're asked to evaluate $27a + 28b + 29c + 30d$, and $27a + 28b + 29c + 30d=30(a+b+c+d)-(3a+2b+c)$.
So now our effort should be focused on finding the value for $3a+2b+c$.
Since $4(63)=252=262-10$, we could write
$4(a+ b + c + d)=a + 2b + 3c + 4d-10$
$3a+ 2b + c=-10$
and therefore $27a + 28b + 29c + 30d=30(63)-(-10)=1900$.
A magician never shows how they do their tricks (Bigsmile)MarkFL said:(Wait) Thanks, but...I left out the part where I explicitly solved a 4X4 linear system to determine what I needed to multiply the equations by so that I got what I needed. (Angel)
The expression evaluates to a value that depends on the values of a, b, c, and d. Without knowing the values of these variables, the expression cannot be simplified further.
To evaluate the expression, you must substitute the values of the variables a, b, c, and d into the expression and then perform the necessary operations. For example, if a = 2, b = 3, c = 4 and d = 5, then the expression would evaluate to 27(2) + 28(3) + 29(4) + 30(5) = 54 + 84 + 116 + 150 = 404.
No, the expression cannot be simplified further without knowing the values of the variables. However, you can combine like terms if the variables have the same coefficients. For example, if the expression was 2a + 2a + 3b + 3b, it could be simplified to 4a + 6b.
The order of operations, also known as PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction), must be followed when evaluating this expression. In this case, the expression does not contain any parentheses or exponents, so you would evaluate the multiplication and division from left to right before evaluating the addition and subtraction.
The expression could be used in a variety of real-life situations, such as calculating the total cost of a shopping trip where a, b, c, and d represent the prices of different items, or determining the total amount of money earned by an employee where a, b, c, and d represent different types of bonuses or incentives. The values of the variables would depend on the specific situation.