Your little sister has made up a card game where different types of cards are worth different points. Face cards are worth 12 points, cards with red numbers are worth 5 points, and cards with black numbers are worth 9 points. Let F be the number of face cards in your hand, R be the number of cards with red numbers in your hand, and B be the number of cards with black numbers in your hand. What algebraic expression models the total number of points that you have in your hand?
Suppose you have 3 face cards, 6 cards with red numbers, and 8 cards with black numbers. How many points do you have?
Responses:
a) 12F + 5R + 9B; 138
b) 3F + 6R + 8B; 153
c) 12F + 5R + 9B; 153
d) 3F + 6R + 8B; 138
The correct algebraic expression that models the total number of points is 12F + 5R + 9B.
Plugging in the given values, we have:
12(3) + 5(6) + 9(8) = 36 + 30 + 72 = 138.
Therefore, the correct answer is option d) 3F + 6R + 8B; 138.
The correct response is c) 12F + 5R + 9B; 153.
To find the algebraic expression that models the total number of points in your hand, you add up the points for each type of card. In this case, face cards are worth 12 points, cards with red numbers are worth 5 points, and cards with black numbers are worth 9 points. Therefore, the expression is 12F + 5R + 9B.
Using the given values for F, R, and B (3, 6, and 8 respectively), you can substitute these values into the expression to find the total number of points in your hand:
12(3) + 5(6) + 9(8) = 36 + 30 + 72 = 138
So, the correct answer is c) 12F + 5R + 9B; 138.