Athor8133idn
Answered

Find the best answers to your questions with the help of IDNLearn.com's knowledgeable users. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.

Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression [tex][tex]$12x^2 - 2xy + 3$[/tex][/tex]. The friends have already collected the following number of cans:

- Jessa: [tex][tex]$3x^2$[/tex][/tex]
- Tyree: [tex][tex]$5x^2 - 8$[/tex][/tex]
- Ben: [tex][tex]$2xy + 4$[/tex][/tex]

Part A:
Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)

Part B:
Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)

Sagot :

GinnyAnsweridn
Certainly! Let's solve the problem step-by-step.

### Part A: Total Canned Food Collected So Far

To determine the total number of canned food items collected by all three friends, we need to sum up the canned food collected by Jessa, Tyree, and Ben.

1. Jessa's Contribution:
[tex]\[ 3x^2 \][/tex]

2. Tyree's Contribution:
[tex]\[ 5x^2 - 8 \][/tex]

3. Ben's Contribution:
[tex]\[ 2xy + 4 \][/tex]

Now, we add these expressions together:
[tex]\[ 3x^2 + (5x^2 - 8) + (2xy + 4) \][/tex]

Combine like terms:
[tex]\[ 3x^2 + 5x^2 + 2xy - 8 + 4 \][/tex]

[tex]\[ (3x^2 + 5x^2) + 2xy + (-8 + 4) \][/tex]

[tex]\[ 8x^2 + 2xy - 4 \][/tex]

So, the total number of cans collected so far is:
[tex]\[ 8x^2 + 2xy - 4 \][/tex]

### Part B: Cans Still Needed to Meet the Goal

The goal for the total number of canned food items is represented by the expression:
[tex]\[ 12x^2 - 2xy + 3 \][/tex]

Now, we need to find out how many more cans need to be collected. This can be done by subtracting the amount collected so far (from Part A) from the goal:

[tex]\[ (12x^2 - 2xy + 3) - (8x^2 + 2xy - 4) \][/tex]

Distribute the negative sign through the second expression:
[tex]\[ 12x^2 - 2xy + 3 - 8x^2 - 2xy + 4 \][/tex]

Combine like terms:
[tex]\[ (12x^2 - 8x^2) + (-2xy - 2xy) + (3 + 4) \][/tex]

[tex]\[ 4x^2 - 4xy + 7 \][/tex]

So, the number of cans still needed to meet their goal is:
[tex]\[ 4x^2 - 4xy + 7 \][/tex]

Putting it all together, we have:

### Final Answer

Part A: The total amount of canned food collected so far by the three friends is:
[tex]\[ 8x^2 + 2xy - 4 \][/tex]

Part B: The number of cans the friends still need to collect to meet their goal is:
[tex]\[ 4x^2 - 4xy + 7 \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.