I guess this is what you want:
SELECT
AI.code,
(
AI.signup_limit -
(
SELECT
COUNT(*)
FROM
signups AS S
WHERE
S.activity_code = AI.code
)
) AS swag
FROM
activity_info AS AI
WHERE
info.code IN
(
SELECT
schedule.code
FROM
schedule INNER JOIN variables ON schedule.date = variables.week
) AND
variables.week = signups.date