2001 SMT/Algebra Problems/Problem 3

Problem

Julie has a 12 foot by 20 foot garden. She wants to put fencing around it to keep out the neighbour’s dog. Normal fenceposts cost $ $2$ each while strong ones cost $ $3$ each. If Julie needs one fencepost for every 2 feet and has $ $70$ to spend on fenceposts, what is the greatest number of strong fenceposts she can buy?

Solution

The perimeter is $64$ feet, so Julie needs $32$ fenceposts. Let $x$ be strong fenceposts and $y$ be normal fenceposts; then we have the equations $3x+2y=70$ $x+y=32$ From here, we easily find that $x=\boxed{6}$ .

~ eevee9406

Page

Toolbox

Search

2001 SMT/Algebra Problems/Problem 3

Problem

Solution