Understanding Algebraic Expressions

The video tutorial covers various algebraic concepts, focusing on combining like terms and simplifying expressions. It uses real-world examples, such as calculating the total number of items or costs, to illustrate these concepts. The tutorial also demonstrates how to use the distributive property to simplify expressions and solve problems related to profit calculation, trading cards, and ticket costs. Additionally, it includes exercises on calculating total weight and water capacity using algebraic expressions.

Ryan is buying tissue paper for decorations. If each small package holds X sheets and each large package holds Y sheets, how many sheets does he have if he buys 3 small and 2 large packages?

• 3X + 2Y

• 5X + 2Y

• 3X + 3Y

• 2X + 3Y

If you have 12 goats and you give away 3, how many goats do you have left?

• 9 goats

• 10 goats

• 15 goats

• 12 goats

Which expression is equivalent to 6a - a + 4b?

• 6a - 5b

• 5a - 4b

• 6a + 4b

• 5a + 4b

An athletic store receives an order of jerseys and shorts. If each jersey weighs X ounces and each pair of shorts weighs Y ounces, what is the total weight of 8 jerseys and 12 shorts?

• 8X + 12Y

• 8X + 10Y

• 10X + 12Y

• 20X + 12Y

What is the simplified expression for the profit from selling picture frames if each frame sells for 11 dollars and costs 6 dollars to make, with a booth rental cost of 36 dollars?

• 11f - 6f

• 11f + 6f - 36

• 5f + 36

• 5f - 36

If the price of a frame increases to 13 dollars, what is the new expression for the profit?

• 7f - 36

• 13f + 6f - 36

• 13f - 6f

• 7f + 36

Nina and Carissa are collecting trading cards. If Nina has 4 packs of Castle cards and 5 packs of Hero cards, and Carissa has 6 packs of Castle cards and 4 packs of Hero cards, what is the total number of Castle cards if each pack holds C cards?

• 9C

• 11C

• 10C

• 8C

An adult ticket to a corn maze costs 4 more than a child ticket. If a child ticket costs C dollars, what is the cost of an adult ticket?

• C + 3

• 4C

• C - 4

• C + 4

If a senior ticket costs 3 more than a child ticket, what is the expression for the cost of a senior ticket?

• 3C

• C + 4

• C + 3

• C - 3

A swimming pool holds 15 times as much water as a waiting pool. If the waiting pool holds G gallons, what is the total amount of water in both pools?

• G + 16

• 15G

• G + 15

• 16G