You and your three friends are going to the State Fair. It costs $5 per person for admission into the fair and $3 for each ride. Which algebraic expression represents the TOTAL amount of money it will cost for you and your three friends to get into the fair and ride "x" amount of rides? (2 points)
Responses
15x
3x + 20
3x + 5
5x + 3
The correct algebraic expression that represents the total amount of money it will cost for you and your three friends to get into the fair and ride "x" amount of rides is:
3x + 20.
Question 2
At the fair there are two bean bag toss games. You gain 3/4 of a point for each bean bag that you get on the target and you lose 1/2 point for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 3/4h - 1/2g. In a different bean bag toss game you gain 7/8 points for each bean bag that get on the target and you lose 3/4 points for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 7/8h - 3/4g. You can figure out the total number of points earned by simplifying this expression: (3/4h - 1/2g) + (7/8h - 3/4g). What would this expression be simplified? (Hint: Combine like terms!) (2 points)
Responses
10/14h - 4/6g
15/8h + 5/4g
1 5/8h - 1 1/4g
1 1/2h - 1 3/4g
To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), we need to combine like terms:
(3/4h + 7/8h) - (1/2g + 3/4g)
To combine the "h" terms, we need to find a common denominator:
(6/8h + 7/8h) - (4/8g + 6/8g)
13/8h - 10/8g
Simplifying the expression, we get:
(13/8h - 10/8g)
Therefore, the simplified expression is 15/8h - 5/4g
The correct response is 15/8h + 5/4g.
Complete this fill-in-the-blank problem. (4 points)
When you evaluate an expression, you substitute a number in for a
. For example, to evaluate the expression 4y+3 for y=6, you would substitute 6 for "y". You would then solve using the Order of Operations. So, 4(6)+3=
. You can also simplify algebraic expressions without knowing what the variables equal. For example, in this expression, (6k+5)+(3k-7). You would add together the coefficients (numbers) in front of "k" and add together the constants or numbers. Adding or subtracting the same variables together is called combining
. So, you would combine 6k + 3k which would equal 9k and you would combine the constants, 5 + -7 which would equal
When you evaluate an expression, you substitute a number in for a variable. For example, to evaluate the expression 4y+3 for y=6, you would substitute 6 for "y". You would then solve using the Order of Operations. So, 4(6)+3=27. You can also simplify algebraic expressions without knowing what the variables equal. For example, in this expression, (6k+5)+(3k-7). You would add together the coefficients (numbers) in front of "k" and add together the constants or numbers. Adding or subtracting the same variables together is called combining like terms. So, you would combine 6k + 3k which would equal 9k and you would combine the constants, 5 + -7 which would equal -2.
At the State Fair you buy 4 combo meals for you and your three friends. Each meal comes with 3 chicken tenders and 2 fried Oreos. How many chicken tenders and fried Oreos do you buy all together? How could you set up and solve this problem using the Distributive Property? (3 points)
To find the total number of chicken tenders and fried Oreos you buy all together, you can multiply the number of combo meals by the number of chicken tenders and fried Oreos in each meal.
Each combo meal comes with 3 chicken tenders and 2 fried Oreos. So, for 4 combo meals, you would have:
4 combo meals * (3 chicken tenders + 2 fried Oreos)
Using the Distributive Property, you can distribute the multiplication to each term inside the parentheses:
4 combo meals * 3 chicken tenders + 4 combo meals * 2 fried Oreos
Then, you can simplify:
12 chicken tenders + 8 fried Oreos
Therefore, you would buy 12 chicken tenders and 8 fried Oreos all together.
At the State Fair it costs $2.75 for a corndog and $3.50 for a funnel cake. How much would it cost for you to order "c" corndogs and "f" funnel cakes? Show how to set this up as an algebraic expression.
Part 2: You and your three friends want to order 2 corndogs and 1 funnel cake each. Solve to find out how much it would cost all-together.
Part 3: Explain how you solved Part 2.
To set up the total cost for ordering "c" corndogs and "f" funnel cakes, you would multiply the cost of each item by the respective quantities and then add them together:
Total cost = (Cost per corndog * Quantity of corndogs) + (Cost per funnel cake * Quantity of funnel cakes)
So, in this case, the algebraic expression would be:
Total cost = (2.75c) + (3.50f)
Part 2:
To find out how much it would cost for you and your three friends to order 2 corndogs and 1 funnel cake each, we can substitute the values into the algebraic expression:
Total cost = (2.75*2) + (3.50*1)
Simplifying, we get:
Total cost = 5.50 + 3.50
Total cost = 9
Therefore, it would cost $9 all together for you and your three friends to order 2 corndogs and 1 funnel cake each.
Part 3:
To solve Part 2, we substituted the given quantities (2 corndogs and 1 funnel cake each) into the expression. We then performed the multiplication and addition to find the total cost.
To determine the algebraic expression that represents the total amount of money it will cost for you and your three friends to get into the fair and ride "x" amount of rides, we need to add the cost of admission for all four people to the cost of the rides.
The cost of admission for each person is $5, so for four people, it will be 4 * $5 = $20.
The cost of each ride is $3, and since you want to ride "x" amount of rides, the total cost of the rides will be $3 * x = $3x.
Therefore, the total cost, which is the sum of the admission cost and the rides cost, can be represented by the algebraic expression:
Cost = 20 + 3x
So, the correct choice for the expression is 3x + 20.