How do you know when you need to use renaming when subtracting mixed numbers?

Cups = c
Plates = p

6p + 5c = 23.80 ==> multiply by 6 ==> 36p + 30c = 142.80
7p + 6c = 28.00 ==> multiply by 5 ==> 35p + 30c = 140.00

Now use algebra to have the 30c be on one side and the rest on the other:

36p + 30c = 142.80 | -36p

30c = 142.80 - 36p

35p + 30c = 140.00 | -35p

30c = 140.00 - 35p

Now set them equal to each other about the 30c:

142.80 - 36p = 140.00 - 35p

Use algebra to solve for p:

142.80 - 36p = 140.00 - 35p | +36p

142.80 = 140.00 + p | - 140

2.80 = p

Go back to one of the "30c" equations and plug in the value for p:

30c = 140 - 35p

30c = 140 - 35(2.80)

30c = 140 - 98

30c = 42 | /30

c = 42/30

c = 1.4

Plates are $2.80
Cups are $1.40

7 0

3 years ago

At age 12 Patrick weighed 43 kg; at age 14 he weighed 50 kg. Patrick’s age and weight are related. A) find a linear equation rel

sergiy2304 [10]

Answer:

A) The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B) The Patrick's age is 10.57 years when he weighed 38 kg

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) and (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The form of the linear equation is y = mx + c, where m is the slope of

the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

* Lets solve the problem

- At age 12 Patrick weighed 43 kg

- At age 14 he weighed 50 kg

- Represent the age by x and the weight by y

∴ There are two points on the line which represents the relation

between the age and the weight of Patrick

∵ (12 , 43) and (14 , 50) belong to the equation relating Patrick’s

weight to his age

A)

- Lets find the equation

∵ (x1 , y1) is (12 , 43) and (x2 , y2) is (14 , 50)

∴ x1 = 12 , x2 = 14 and y1 = 43 and y2 = 50

∴ $m=\frac{50-43}{14-12}=\frac{7}{2}$

∵ y = mx + c

∴ y = 7/2 x + c

- To find c by substitute x and y in the equation by the coordinates

of one of the 2 points

∵ 43 = 7/2 (12) + c

∴ 43 = 42 + c

- Subtract 42 from both sides

∴ c = 1

∴ The equation is y = 7/2 x + 1

* The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B)

∵ The weight of Patrick is 38 kg

- That means y = 38

∵ y = 7/2 x + 1

∴ 38 = 7/2 x + 1

- Subtract 1 from both sides

∴ 37 = 7/2 x

- Divide both sides by 7/2

∴ x = 37 ÷ 7/2 = 10.57

∴ The Patrick's age is 10.57 years when he weighed 38 kg

5 0

3 years ago