Problem number 14. We are given five numbers, a1, a2, a3, a4, a5, whose sum is s. For each k, 1 is less than or equal to k is less than or equal to 5. We know that ak is equal to k plus s. What is the value of s? So right away, we notice some symmetry in the equation. So first of all, by definition, we're given that the sum a1 plus a2 plus a3 plus a4 plus a5 is equal to s. And we're also given five equations, a1 is equal to 1 plus s, a2 is equal to 2 plus s, and so on until a5 is equal to 5 plus s. And now we can combine all this to really figure out that value of s. We won't even need to find the value of a1 through a5, we can just use the equations that they give us. If you plug in 1 plus s for a1, 2 plus s for a2, and so on, and plug in 3 plus s for a3, all the way to a5, we get that 1 plus 2 plus 3 plus 4 plus 5 plus 5s is equal to s. Now we just have a linear equation with one variable, and that's not that hard to solve. So we can just combine, isolate the s, and get that s is equal to negative 15 over 4. So our correct answer is b.

sum problem

linear equation

symmetry

solve for s

negative 15 over 4