Final answer:
To create an algebraic expression where x=3 and y=5 results in 50, one can use a linear relationship formula. Selecting coefficients that satisfy the equation 50 = ax + by, setting a=10 and b=5, the expression 10x + 5y is obtained and meets the required condition.
Step-by-step explanation:
To write an algebraic expression with two variables, x, and y, that equals 50 when x=3 and y=5, we need to find coefficients that will satisfy this condition. One way to do this is to assume that the relationship between x and y is linear and can be represented by an equation of the form y = mx + b, where m and b are constants.
Let's form an equation:
y = mx + b
Substituting the given values, we have:
5 = m(3) + b
To solve for m and b, we can use another condition in the expression equals 50. If we consider another equation 50 = ax + by, where a and b are again constants, we can substitute x=3 and y=5 to get:
50 = a(3) + b(5)
From this equation, we can pick suitable values for a and b to satisfy the condition. For example, we could choose a=10 and b=5. Substituting these into our equation, we get:
50 = 10(3) + 5(5)
Which simplifies to:
50 = 30 + 25
Therefore the algebraic expression that satisfies the given conditions is 10x + 5y.