Question

The sum of two numbers is 44. The second number is 4 less than three times the first number. Let x represent the first number and let y represent the second number. If the table will be used to guess and check, what should the equation be at the top of the last column?

Answer 1

The equation x + (3x - 4) = 44 should be at the top of the last column

Step-by-step explanation:

The given is:

• The sum of two numbers is 44
• The second number is 4 less than three times the first number
• x represent the first number and let y represent the second number

We need to find that If the table will be used to guess and check, what should the equation be at the top of the last column

∵ The 1st number is x

∵ The 2nd number is y

∵ The sum of the two numbers is 44

- Add x , y and equate the sum by 44

∴ x + y = 44 ⇒ (1)

∵ The second number is 4 less than three times the first number

- That means y is less than 3 times x by 4

∴ y = 3x - 4 ⇒ (2)

Now we have a system of equation

Substitute y in equation (1) by equation (2)

∵ x + (3x - 4) = 44 ⇒ (3)

- Add like terms in the left hand side

∴ 4x - 4 = 44

- Add 4 from both sides

∴ 4x = 48

- Divide both sides by 4

∴ x = 12

- Substitute the value of x in equation (2) to find y

∵ y = 3(12) - 4

∴ y = 36 - 4 = 32

∴ The two numbers are 12 and 32

The equation that can used in the table of guess and check is the equation after substitute the value of y by x, equation (3)

∴ The equation of the last column is x + (3x - 4) = 44

- Guess that x = 10, then 10 + (3 × 10 - 4) = 10 + 26 = 36 less than 44

- Guess that x = 11, then 11 + (3 × 11 - 4) = 11 + 29 = 40 less than 44

- Guess that x = 12, then 12 + (3 × 12 - 4) = 12 + 32 = 44

- Then x = 12 and y = 32

The equation x + (3x - 4) = 44 should be at the top of the last column

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Answer 2

Answer:

y=3x-4

Step-by-step explanation:

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