One number is five times another number. their sum is 42. what are the two numbers?

After solving the above word sentence, the two numbers are 35 and 7 respectively.

In this exercise, you're required to find two numbers by translating the word sentence into an algebraic expression and then solving for the unknown variables (a and b).

Translating the word sentence into an algebraic expression, we have;

One number is five times another number:

 .....equation 1

Their sum is 42:

  ...equation 2

Substituting eqn 1 into eqn2, we have:

b = 7

To find the first number:

a = 35

Therefore, the two numbers are 35 and 7 respectively.

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7 and 35

Step-by-step explanation:

Let one number be x and the other number be y

"one number is five times another number"

Expressed mathematically: y = 5x --- -eq 1

"their sum is 42"

Expressed mathematically : x + y = 42 eq2

Now we have a system of equations with 2 equations and 2 unknowns, we can solve this easily by substitution

From equation 2,

x + y = 42   (substitute eq 1 into eq 2)

x + (5x) = 42

6x = 42   (divide both sides by 6)

x = 42/6 = 7 (answer)

substituting this back into equation 1:

y = 5x

y = 5(7)

y = 35 (answer)

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.