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faust18 [17]
3 years ago
11

40 in the ratio 2:3 £2000 in the ratio 3:7 36kg in the ratio 1:2:3

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
8 0
Answer:
a) 16: 24
b)  £600 : £1400
c)  6 : 12 : 18


40 in the ratio 2 : 3 

To split an amount based on ratio 2:3 , first, we need to find the total share.

-------------------------------------------------
Find total shares
-------------------------------------------------
2+3 = 5

Then we need to find the the amount of 1 share worth 

-------------------------------------------------
Find 1 share
-------------------------------------------------
5 shares = 40                ← divide by 5 on both sides
÷ 5             ÷ 5 
1 share = 8 

Now that we know one share is 8, we need to find the amount according to the shares allocation, which is 2 and 3 in this question.

-------------------------------------------------
Find 2 shares
-------------------------------------------------
1 share = 8                    ← multiply by 2 on both sides
x2           x2
2 shares = 16

-------------------------------------------------
Find 3 shares
-------------------------------------------------
1 share = 8
x3            x3
3 shares = 24

The ratio is 2 : 3. The 40 is therefore the amount split as 16:24

-------------------------------------------------
Answer: 16: 24
-------------------------------------------------

£2000 in the ratio 3: 7

To split the £2000 into the ratio 3:7, first, we need to find the total shares.

-------------------------------------------------
Find total shares
-------------------------------------------------
3 + 7 = 10

Then we find the 1 share worth
-------------------------------------------------
Find 1 share
-------------------------------------------------
10 shares = £2000              ← divide by 10 on both sides
÷10              ÷10
1 share = £200

Now that we know 1 share is worth £200, we need to find the shares according to the ratio allocation.

-------------------------------------------------
Find 3 shares
-------------------------------------------------
1 share = £200                    ← multiply 3 on both sides
x3             x3
3 shares = £600

-------------------------------------------------
Find 7 shares
-------------------------------------------------
1 share = £200                         ← multiply by 7 on both sides
x7            x7
7 shares = £1400

The ratio 3 : 7, the £2000 is spilt into £600 : £1400

-------------------------------------------------
Answer: £600 : £1400
------------------------------------------------

36 kg into the ratio 1:2:3

To spilt the 36kg, first we find the total number of shares

------------------------------------------------
Find total shares
------------------------------------------------
1 + 2 + 3 = 6

36 kg is split into 6 shares. We need to find the allocation of 1 share.
------------------------------------------------
Find 1 share
------------------------------------------------
6 shares = 36              ← divide by 6 on both sides
÷6             ÷6
1share = 6kg

The allocation of 1 share is 6kg. Now find 2 shares and 3 shares

------------------------------------------------
Find 2 shares
------------------------------------------------
1 share = 6kg                 ← multiply by2 on both sides
x2            x2
2 shares = 12kg

------------------------------------------------
Find 3 shares
------------------------------------------------
1 share = 6 kg            ← multiply by 2 on both sides
x3            x3
3shares = 18kg

The ratio is 1:2:3. 36kg is spilt into 6: 12: 18

------------------------------------------------
Answer: 6 : 12 : 18
------------------------------------------------


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x2−8x+15

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We need two numbers that...

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Can you think of the two numbers?

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Answer:

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Step-by-step explanation:

Given D(3, 2 ) → D'(2, 4 )

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3 years ago
Charlie does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at lea
german

Answer:

(x_1,y_1) = (0,9)

(x_2,y_2) = (6,3)

(x_3,y_3) = (6,12)

Step-by-step explanation:

Given

x = hours spent on cardiovascular work

y = hours spent on weight training

From the first statement,

Each week: he spends at least 9 hours

This is represented as:

Total \ge 9

x + y \ge 9

From the second statement,

Each week: he spends a max of 12 hours on weights

This is represented as:

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From the third statement,

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This is represented as:

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x \le 6

So, the inequalities are:

x + y \ge 9

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See attachment for the graph where the solution are also highlighted

From the attachment, the solutions are:

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(x_3,y_3) = (6,12)

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