66 bats were sold. some were sold for $42 each. the rest were on sale for $30 each. total sale were $2,460. write and solve a system of equations to find out how many bats were sold at $42 each

40 bats were sold at $ 42 each

Solution:

Let "x" be the number of bats sold at $ 42 each

Let "y" be the number of bats sold at $ 30 each

Totally 66 bats were sold. Therefore, we can say,

bats sold at $ 42 each + bats sold at $ 30 each = 66

x + y = 66 ---------- eqn 1

Total sale were $2,460

Therefore, a equation is framed as:

number of bats sold at $ 42 each x price of 1 bat + number of bats sold at $ 30 each x price of 1 bat = 2460

42x + 30y = 2460 ----------- eqn 2

Let us solve eqn 1 and eqn 2,

From eqn 1,

x = 66 - y --------- eqn 3

Substitute eqn 3 in eqn 2

42(66 - y) + 30y = 2460

2772 - 42y + 30y = 2460

-12y = 2460 - 2772

-12y = -312

Substitute y = 26 in eqn 3

x = 66 - 26

Thus 40 bats were sold at $ 42 each

she will travel a distance in the range of 3 - 11 miles