Math / Algebra

Question16 Watsan, Mizhane
A grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.
Which inequality represents all possible combinations of $x$ , the number of sausage links that will be cooked on the grill, and $y$ , the number of briskets that will also be cooked? (A) $6 x+2 y<120$ (B) $6 x+2 y>120$ (c) $2 x+6 y \leq 120$ (D) $2 x+6 y \geq 120$

Studdy Solution

STEP 1

What is this asking? How many 2 lb sausages ( $x$ ) and 6 lb briskets ( $y$ ) can we cook on a grill, if the total weight can't be more than 120 lb? Watch out! Don't mix up the weights of the sausages and briskets!
Also, pay close attention to whether the inequality should be less than or equal to, or greater than or equal to.

STEP 2

1. Write the weight of sausages.
2. Write the weight of briskets.
3. Write the total weight inequality.

STEP 3

Each sausage link weighs $2$ lb, and we're cooking $x$ sausages.
So, the total weight of the sausages is $2 \cdot x$ lb.
Easy peasy!

STEP 4

Each brisket weighs $6$ lb, and we have $y$ briskets.
So, all those delicious briskets weigh $6 \cdot y$ lb.

STEP 5

We know the total weight of sausages and briskets cannot be more than 120 lb.
This means the total weight must be less than or equal to 120 lb.

STEP 6

The total weight of sausages ( $2 \cdot x$ ) plus the total weight of briskets ( $6 \cdot y$ ) must be less than or equal to 120 lb.
This gives us the inequality: $2 \cdot x + 6 \cdot y \leq 120$

STEP 7

The inequality that represents all possible combinations of $x$ sausage links and $y$ briskets is $2x + 6y \leq 120$ , which is answer (C).
Boom!

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Studdy Solution

STEP 1

STEP 2

1. Write the weight of sausages.
2. Write the weight of briskets.
3. Write the total weight inequality.

STEP 3

Each sausage link weighs $2$ lb, and we're cooking $x$ sausages.
So, the total weight of the sausages is $2 \cdot x$ lb.
Easy peasy!

STEP 4

Each brisket weighs $6$ lb, and we have $y$ briskets.
So, all those delicious briskets weigh $6 \cdot y$ lb.

STEP 5

We know the total weight of sausages and briskets cannot be more than 120 lb.
This means the total weight must be less than or equal to 120 lb.

STEP 6

The total weight of sausages ( $2 \cdot x$ ) plus the total weight of briskets ( $6 \cdot y$ ) must be less than or equal to 120 lb.
This gives us the inequality: $2 \cdot x + 6 \cdot y \leq 120$

STEP 7

The inequality that represents all possible combinations of $x$ sausage links and $y$ briskets is $2x + 6y \leq 120$ , which is answer (C).
Boom!

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Studdy Solution

STEP 1

STEP 2

1. Write the weight of sausages.2. Write the weight of briskets.3. Write the total weight inequality.

STEP 3

Each sausage link weighs 222 lb, and we're cooking xxx sausages.So, the **total weight** of the sausages is 2⋅x2 \cdot x2⋅x lb.Easy peasy!

STEP 4

Each brisket weighs 666 lb, and we have yyy briskets.So, all those delicious briskets weigh 6⋅y6 \cdot y6⋅y lb.

STEP 5

We know the total weight of sausages and briskets *cannot* be more than 120 lb.This means the total weight must be *less than or equal to* 120 lb.

STEP 6

The **total weight** of sausages (2⋅x2 \cdot x2⋅x) *plus* the **total weight** of briskets (6⋅y6 \cdot y6⋅y) must be less than or equal to 120 lb.This gives us the inequality: 2⋅x+6⋅y≤1202 \cdot x + 6 \cdot y \leq 1202⋅x+6⋅y≤120

STEP 7

The inequality that represents all possible combinations of xxx sausage links and yyy briskets is 2x+6y≤1202x + 6y \leq 1202x+6y≤120, which is answer (C).Boom!

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1. Write the weight of sausages.
2. Write the weight of briskets.
3. Write the total weight inequality.

Each sausage link weighs $2$ lb, and we're cooking $x$ sausages.
So, the total weight of the sausages is $2 \cdot x$ lb.
Easy peasy!

Each brisket weighs $6$ lb, and we have $y$ briskets.
So, all those delicious briskets weigh $6 \cdot y$ lb.

We know the total weight of sausages and briskets cannot be more than 120 lb.
This means the total weight must be less than or equal to 120 lb.

The total weight of sausages ( $2 \cdot x$ ) plus the total weight of briskets ( $6 \cdot y$ ) must be less than or equal to 120 lb.
This gives us the inequality: $2 \cdot x + 6 \cdot y \leq 120$

The inequality that represents all possible combinations of $x$ sausage links and $y$ briskets is $2x + 6y \leq 120$ , which is answer (C).
Boom!