Keith has $500 in a savings account at the beginning of the summer. He withdraws $25 each week for food, clothes, and movie tickets. He wants to have an account balance of at least $200 in the account at the end of the summer.

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the inequality is 500 - 25x >= 200

this insures that he will have at least 200 at the end of the summer.

subtract 200 from both sides of that inequality and add 25x to both sides of that inequality to get 500 - 200 >= 25x

simplify to get 300 >= 25x

divide both sides of that equation by 25 to get 300 / 25 >= x

simplify to get 12 >= x

12 >= x means x <= 12.

when x is smaller than or equal to 12, he will be guaranteed to have at least 200 in the account at the end of the summer.

when x = 12, what is left in the account is 500 - 25 * 12 = 200.

when x = 11, what is left in the account is 500 - 25 * 11 = 225.

when x = 13, what is left in the account is 500 - 25 * 13 = 175.

the maximum number of weeks he can withdraw money from his account is 12.

Step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2