A farmer has 4 times as many ducks as chickens. There are 72 more chickens than ducks. How many chickens and ducks does the farmer have altogether?

The farmer has 120 birds altogether

Step-by-step explanation:

Now, since the number of chickens us equal to 4 times the number of ducks, it means that if there are 2 ducks, there are (2 × 4) chickens and if there are 5 ducks in the farm, there are (5 × 4) chickens.

Let's then denote the number of ducks by "b". So, if the number of chickens is equal to 4 times the number of ducks, then the total quantity of birds belonging to the farmer

= 4b + b

If there are 72 more chickens than ducks, the quantity of birds is:

4b - b = 72

3b = 72

b = 72/3

b = 24 ducks

Since 4b represents the quantity of chickens and b is equal to 24, then the actual quantity of chickens = 4 × 24 = 96.

Therefore, if there are 96 chickens and 24 ducks in the farm, then the actual sum of the birds belonging to the farmer is:

96 + 24

= 120 birds

The farmer has 120 birds altogether.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: