Question

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation? 2 x minus y = negative 6 and 3 x minus y = negative 5 2 x minus y = negative 3 and 3 x minus y = negative 5 2 x minus y = negative 6 and x minus 3 y = 5 2 x minus y = negative 3 and x minus 3 y = 5

Answer 1

Answer:

2 x minus y = negative 6 and 3 x minus y = negative 5

Step-by-step explanation:

y = 2(x+3) = 2x + 6 or 2x - y = -6

y = 5 + 3x or 3x - y = -5

Answer 2

The equations that represent the situation is: 2 x minus y = negative 6 and 3 x minus y = negative 5

From the given information:

Let the smaller number be x; then the word problem can be expressed as:

• y = 2(x + 3)   ---- (1)
• y = 5 + 3x     ---- (2)

From (1), if we open the brackets, we have:

• y = 2x + 6
• -2x + y = +6

multiplying through by (-), we have:

• 2x - y = -6

Also, from equation (2)

• y = 5 + 3x

By rearrangement

• y - 3x = 5
• -3x + y = 5

Multiplying through by (-), we have:

• 3x - y = -5

Therefore, we can conclude that the equations that represent the situation is: 2 x minus y = negative 6 and 3 x minus y = negative 5

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