To find the final cost for the Goodin family's groceries after using the coupon, we first need to calculate the amount of the discount provided by the coupon.
The original cost of the groceries is $240, and the coupon offers a 20% discount. To find out how much 20% of $240 is, we convert the percentage into a decimal. We do this by dividing 20 by 100, which gives us 0.20.
Next, we multiply the original cost by this decimal to determine the discount amount: \[ 240 \times 0.20 = 48 \] So, the discount is $48.
Now, to find the final cost after applying the coupon, we subtract the discount from the original price: \[ 240 - 48 = 192 \]
Therefore, the final cost of the groceries for the Goodin family, after using the coupon, is $192.