Question

Anna purchased 32 strings forher autoharp. Wrapped strings cost $4.49 each andunwrapped strings cost $2.99 each. If she paid atotal of $107.68 for the strings, how many of eachtype did she buy?

Answer 1

Let Anna bought x number of wrapped strings and y number of unwrapped strings.

Anna purchased 32 strings. Therefore,

x+y=32 (i)

Again, Wrapped strings cost $4.49 each and unwrapped strings cost $2.99 each and she paid total $107.68

Therefore,

4.49x+2.99y=107.68 (ii)

Now, let us solve the system of linear equations (i) and (ii).

The two lines intersect each other at the point (8,24).

Therefore, the solution is

x=8

y=24

Hence, Anna bought 8 wrapped strings and 24 unwrapped strings