Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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]\(10x^2 - 4xy + 12\)[/tex]. The friends have already collected the following number of cans:

- Jessa: [tex]\(7xy + 3\)[/tex]
- Tyree: [tex]\(3x^2 - 4\)[/tex]
- Ben: [tex]\(5x^2\)[/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 :

GinnyAnswer
To tackle this question, let's break it down into two parts as specified.

### Part A: Expression for the Amount of Canned Food Collected So Far

Firstly, we need to find the amount of canned food each friend has collected.

1. Jessa's contribution:
[tex]\(7xy + 3\)[/tex]

2. Tyree's contribution:
[tex]\(3x^2 - 4\)[/tex]

3. Ben's contribution:
[tex]\(5x^2\)[/tex]

Next, we sum these individual contributions to find the total amount collected so far:

[tex]\[ (7xy + 3) + (3x^2 - 4) + (5x^2) \][/tex]

We then combine like terms in the expression:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 5x^2 = 8x^2\)[/tex]
- Combine the [tex]\(xy\)[/tex] terms: [tex]\(7xy\)[/tex] (no other [tex]\(xy\)[/tex] terms to combine with)
- Combine the constant terms: [tex]\(3 - 4 = -1\)[/tex]

Therefore, the total amount of canned food collected so far by the three friends is:

[tex]\[ 8x^2 + 7xy - 1 \][/tex]

### Part B: Expression for the Number of Cans Still Needed to Meet the Goal

The collection goal is expressed as:
[tex]\[ 10x^2 - 4xy + 12 \][/tex]

We have already calculated the total amount collected so far as:
[tex]\[ 8x^2 + 7xy - 1 \][/tex]

To find the number of cans still needed, we subtract the total collected amount from the goal. Thus, the expression for the number of additional cans required is:

[tex]\[ (10x^2 - 4xy + 12) - (8x^2 + 7xy - 1) \][/tex]

Now, let's simplify this expression by distributing the negative sign and combining like terms:

[tex]\[ 10x^2 - 4xy + 12 - 8x^2 - 7xy + 1 \][/tex]

Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 10x^2 - 8x^2 = 2x^2 \][/tex]

Combine the [tex]\(xy\)[/tex] terms:
[tex]\[ -4xy - 7xy = -11xy \][/tex]

Combine the constant terms:
[tex]\[ 12 + 1 = 13 \][/tex]

Therefore, the expression that represents the number of cans the friends still need to collect is:

[tex]\[ 2x^2 - 11xy + 13 \][/tex]

### Summary
- Part A: The quantity of canned food collected so far by the three friends is: [tex]\( 8x^2 + 7xy - 1 \)[/tex]
- Part B: The number of additional cans needed to meet their goal is: [tex]\( 2x^2 - 11xy + 13 \)[/tex]

This completes our detailed solution for both parts of the question.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.