John Math Midterm Practice

James weighs 30 pounds more than Nathan. Together, they weigh 130 pounds. Write and solve an algebraic equation to find how much James weighs.

• 80 pounds

• 90 pounds

• 100 pounds

• 110 pounds

Answer explanation

Let Nathan's weight be x. Then, James's weight is x + 30. Together, they weigh 130 pounds: x + (x + 30) = 130. Solving gives 2x + 30 = 130, so 2x = 100, and x = 50. Thus, James weighs 50 + 30 = 80 pounds.

Factor: 17abcd - 51ab

• ab(17cd - 51)

• ab(17c - 3)

• ab(17d - 3)

• ab(17c - 51)

Answer explanation

To factor 17abcd - 51ab, first factor out the common term ab. This gives us ab(17cd - 51), which matches the correct choice. The other options do not correctly represent the factored form.

Combine the following: (3x - 4y + 5z) - (6z + 2y - 4x)

• 7x - 6y - z

• 7x - 2y - z

• x - 6y - z

• x - 2y - z

Answer explanation

To combine (3x - 4y + 5z) - (6z + 2y - 4x), distribute the negative sign: 3x - 4y + 5z - 6z - 2y + 4x. Combine like terms: (3x + 4x) + (-4y - 2y) + (5z - 6z) = 7x - 6y - z. Thus, the correct answer is 7x - 6y - z.

Combine the following: (3x - 4y + 5z) + (6z + 2y - 4x)

• -x - 2y + 11z

• -x - 6y + 11z

• x - 2y + 11z

• x - 6y + 11z

Answer explanation

To combine (3x - 4y + 5z) + (6z + 2y - 4x), first group like terms: (3x - 4x) + (-4y + 2y) + (5z + 6z) = -x - 2y + 11z. Thus, the correct answer is -x - 2y + 11z.

What is the algebraic expression for "7 less than a number, n"?

• n + 7

• n - 7

• 7n

• 7 - n

Answer explanation

The phrase '7 less than a number, n' means you subtract 7 from n. Therefore, the correct algebraic expression is n - 7.

How would you express "Four times a number, k, increased by 5 is 12" in an equation?

• 4k + 5 = 12

• 4k - 5 = 12

• 5k + 4 = 12

• 4 + 5k = 12

Answer explanation

The phrase "Four times a number, k, increased by 5 is 12" translates to the equation 4k + 5 = 12, where 4k represents four times the number k, and adding 5 gives the total of 12.

What is the expression for "The sum of two numbers, a and b"?

• a - b

• ab

• a + b

• a/b

Answer explanation

The phrase 'The sum of two numbers, a and b' directly translates to the mathematical operation of addition, which is represented as 'a + b'. Therefore, the correct expression is 'a + b'.

How do you write "Twice the difference of two numbers, p and r" as an expression?

• 2(p + r)

• 2(p - r)

• p - 2r

• 2pr

Answer explanation

The phrase 'Twice the difference of two numbers, p and r' means you first find the difference (p - r) and then multiply it by 2. Thus, the expression is 2(p - r), making it the correct choice.

What is the equation for "The product of 3 and a number, d, is 20"?

• 3d = 20

• 3 + d = 20

• 3d + 20

• d/3 = 20

Answer explanation

The phrase 'The product of 3 and a number, d, is 20' translates mathematically to 3 multiplied by d, which is expressed as 3d. Therefore, the correct equation is 3d = 20.

How would you express "6 more than three times a number, f"?

• 3f + 6

• 6f + 3

• 3(f + 6)

• 6 + f/3

Answer explanation

To express '6 more than three times a number, f', you first calculate three times the number, which is 3f, and then add 6. Thus, the correct expression is 3f + 6.