Define variables

Let the original cost of one orange be $x$ and one banana be $y$.

$9x + 8y = 276$

Formulate second equation

When the orange cost decreases by 10%, it becomes $0.9x$. The new equation for 5 oranges and 10 bananas is:

$5(0.9x) + 10y = 210 \implies 4.5x + 10y = 210$

Solve the system of linear equations

Multiply the second equation by 2 to eliminate $y$: $9x + 20y = 420$. Subtract the first equation ($9x + 8y = 276$) from this:

$12y = 144 \implies y = 12$

Find the value of x

Substitute $y = 12$ into the first equation:

$9x + 8(12) = 276 \implies 9x + 96 = 276 \implies 9x = 180 \implies x = 20$

Calculate the required cost

Find the original cost of 3 oranges and 4 bananas:

$3(20) + 4(12) = 60 + 48 = 108$