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Musya8 [376]
1 year ago
10

The weight of Jane and Jessica was in the ratio of 8 : 9. Jane gained 2 kg while Jessica lost 4 kg. They then had the same weigh

t. What was Jane's weight at first?
Mathematics
1 answer:
postnew [5]1 year ago
3 0

Answer:

  48 kg

Step-by-step explanation:

The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.

__

<h3>setup</h3>

Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...

  x/y = 8/9

After the changes in weight, they were equal:

  x+2 = y-4

__

<h3>solution</h3>

Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.

  y = x +6 . . . . . . . . . . solve the second equation for y

  x/(x+6) = 8/9 . . . . . . substitute for y in the first equation

  9x = 8(x +6) . . . . . . . multiply by 9(x+6)

  x = 48 . . . . . . . . . . . simplify and subtract 8x

Jane weighed 48 kg at first.

_____

<em>Alternate solution</em>

The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.

(This mental solution is virtually the same as the solution using equations shown above.)

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saveliy_v [14]

Answer:

Perimeter = 60

Step-by-step explanation:

because l bisects AB:

3y+1 = 5y-5

reduce:

2y = 6

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and:

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reduce:

2x = 16

x = 8

AB = (3y+1) + (5y-5)

AB = 8y-4

substitute for y

AB = 8(3)-4

AB = 20

Perimeter = (2x+4) + (4x-12) + 20

reduce:

perimeter = 6x+12

substitute for x:

Perimeter =6(8)+12

reduce:

Perimeter = 60

3 0
2 years ago
a vegetarian sandwich is in the aproximate shape of a cone. the height of the sandwich is 6 inches and the base diameter is 3.5
Olenka [21]

Answer: 19.2inches³

Step-by-step explanation:

The volume of a cone is calculated as:

= 1/3πr²h

where,

π = 3.14

r = radius = diameter/2 = 3.5/2 = 1.75

h = height = 6

Volume = 1/3πr²h

= 1/3 × 3.14 × 1.75² × 6

= 19.2325

= 19.2inches³

Therefore, the volume of the cone-shaped sandwich is 19.2inches³.

5 0
3 years ago
Subtract. Write your answer as a mixed number in simplest form.<br><br> 8 1/4 + 4 5/6
Tasya [4]

Answer:

13 1/12

Step-by-step explanation:

6 0
3 years ago
Tia and Ken sold snack bars and magazine subscriptions for the school fundraiser. Tia sold 16 snack bars and 4 magazine subscrip
Aliun [14]

Answer:

The value of the snack bar is $ 2 and that of the magazine subscription is 25 $

Step-by-step explanation:

We have a system of two equations and two unknowns, which would be the following:

let "x" be the cost of the snack bar

Let "y" be the cost of the magazine subscription

16 * x + 4 * y = 132

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replacing:

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2.66 * x = 132 - 126.66

x = 5.34 / 2.66

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for "y":

y = (190 - 20 * 2) / 6

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6 0
3 years ago
What is the estimate of 405?
mario62 [17]

Answer:

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Step-by-step explanation:


6 0
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