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JulijaS [17]
3 years ago
5

Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is

available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
Mathematics
1 answer:
NeX [460]3 years ago
5 0

Answer:

You require 10 helpers

Step-by-step explanation:

The problem could be solved in many ways ( like using an optimization software) but I propose you this.

Start with production of large cakes.  In the time kitchen is available one helper could make, if only works in large cakes:

(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes

So with 3 helpers using all their 3 hours we would have

3 helpers *6 large cakes /helper  = 18 large cakes.

We need 2 more large cakes so we can use one more helper and in his first hour he can produce

(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes

The 4th helper has two hours of work left so he can produce small cakes.

(35 small cakes/hour* 2 hours = 70 small cakes.

With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes

700 - 70 = 630 small cakes left

In the 3 hour period a helper can make

(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes

So if 1 helper does  105 large cakes  we would need to finish production with

630 / 105 =  6 helpers

So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers

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Chloe purchased some dried mango and dried kiwi to make some trail mix. The dried mango cost ​$2.11 per pound and the dried kiwi
andreev551 [17]

Answer:

Number of pounds of dried mangoes Chloe bought = 3.5

Number of pounds of dried kiwi Chloe bought bough = 6.5

Step-by-step explanation:

Total number of pounds of dried fruit purchased = 10

Let number of pounds of dried mango purchased = x

Let number of pounds of dried kiwi purchased be = y

Total weight of dried fruits purchased = x+y

So, we have a sum equation as:

x+y=10

Total cost of dried fruits = $40.34

Cost of a pound of dried mango = $2.11

Cost of x pounds of dried mango in dollars can be given as = 2.11x

Cost of a dried kiwi = $5.07

Cost of y pounds of dried kiwi in dollars can be given as = 5.07y

Total cost of dried fruits in dollars = 2.11x+5.07y

So, we have a cost equation as:

2.11x+5.07y=40.34

The system of equations is :

A) x+y=10

B) 2.11x+5.07y=40.34

Solving by substitution.

Rearranging equation A, to solve for y in terms of x

Subtracting both sides by x

x+y-x=10-x

y=10-x

Substituting value of y we got from A into equation B.

2.11x+5.07(10-x)=40.34

Using distribution.

2.11x+50.7-5.07x=40.34

Simplifying.

-2.96x+50.7=40.34

Subtracting both sides by 50.7.

-2.96x+50.7-50.7=40.34-50.7

-2.96x=-10.36

Dividing both sides by -2.96.

\frac{-2.96x}{-2.96}=\frac{-10.36}{-2.96}

∴ x=3.5

We can plugin x=3.5 in the rearranged equation A to get value of y

y=10-3.5

∴ y=6.5

So, number of pounds of dried mangoes Chloe bought = 3.5

Number of pounds of dried kiwi Chloe bought bough = 6.5

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The answer is B. x > -22


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x > -22
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Hello I'm Chloe Can you help me, Thank you :)
andrew-mc [135]

Answer:

b is correct

Step-by-step explanation:

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