Question

Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smaller number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation? y = negative four-thirds x + 31. y = 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = 2 x + 7. y = negative four-thirds x + 31. y = negative 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = negative 2 x + 7.

Answer 1

Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x represent the smaller number and y represent the larger number.

Part 1

Four times a number added to 3 times a larger number is 31.

It is translated as:

• 4x + 3y = 31

Then, solving for y:

• 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

Correct answer choice for this equation:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

Seven subtracted from the larger number is equal to twice the smaller number.

It is translated as:

• y-7= 2x

Then, solving for y:

• y-7= 2x ⇒ y= 2x+ 7

Correct answer choice for this equation:

y = 2 x + 7