Equations in One Variable Quiz

Which equation represents this sentence? Four times the sum of a number x and a number y is equal to 25.

• 4xy = 25

• 4x + y = 25

• 4(x + y) = 25

• 4 + x + y = 25

Answer explanation

The sentence states 'Four times the sum of a number x and a number y', which translates to 4(x + y). This is equal to 25, leading to the equation 4(x + y) = 25, making it the correct choice.

Match each equation to its verbal description. a. The product of three and the sum of x and y is equal to six. ____ b. The product of three times x and y is equal to six. ____ c. The sum of three times x and y is equal to six. ____ d. The sum of three and the product of x and y is equal to six. ____

• (3x)y = 6

• 3x + y = 6

• 3(x + y) = 6

• 3 + xy = 6

Answer explanation

a. 3(x + y) = 6: The product of three and the sum of x and y. b. (3x)y = 6: The product of three times x and y. c. 3x + y = 6: The sum of three times x and y. d. 3 + xy = 6: The sum of three and the product of x and y.

Write a sentence for the equation: 2 + 3n = 5n

Answer explanation

The equation 2 + 3n = 5n can be interpreted as stating that adding 2 to three times a number n equals five times that same number n.

Write an equation to represent this sentence. The difference of twice x and four times the quantity x plus y is equal to ten.

Answer explanation

The sentence describes the equation: 2x - 4(x + y) = 10. Here, 'twice x' is 2x, 'four times the quantity x plus y' is 4(x + y), and 'the difference' indicates subtraction, leading to the equation being equal to ten.

Write a sentence for the below equation. 7(3 + 5n) = an

Answer explanation

The equation 7(3 + 5n) = an represents a situation where 7 times the sum of 3 and 5 times a variable n equals a product of a constant a and the same variable n.

Write a sentence for the equation: 2(x+1) = 10

• The quantity two x plus one is equal to ten.

• Two times the sum of x and one equals ten.

• The quantity two times x plus one is the same as ten.

• The sum of 2x and 1 is 10.

Answer explanation

The correct choice, 'The quantity two x plus one is equal to ten,' accurately reflects the equation 2(x+1) = 10, clearly stating that two times the sum of x and one equals ten.

Write an equation for the below sentence. Three added to four times a number n is the same as 19.

• 3+4n=19

• (3+4)n=19

• 4+3n=19

• (3+4)n=19n

Answer explanation

The sentence states that three added to four times a number n equals 19. This translates to the equation 3 + 4n = 19, making the first answer choice the correct one.

The coldest temperature recorded in Alaska was around –80°F. This was 10°F warmer than the coldest temperature recorded in Siberia. Which equation can be used to find the coldest temperature recorded in Siberia? Find the coldest temperature recorded in Siberia.

• T + 10 = –80; –90°

• T + 10 = –80; –70°

• T – 10 = –80; –90°

• T – 10 = –80; –70°

Answer explanation

To find the coldest temperature in Siberia, let T be that temperature. Since Alaska's coldest is -80°F and it's 10°F warmer than Siberia, the equation is T + 10 = -80. Solving gives T = -90°F, so the correct choice is T - 10 = -80; -70°F.

Hind has walked 2 miles. Her goal is to walk 6 miles. Hind plans to reach her goal by walking 3 miles each hour h for the rest of her walk. Write an equation to find the number of hours it will take Hind to reach her goal.

Answer explanation

Hind has already walked 2 miles, so she has 4 miles left to reach her goal. If she walks 3 miles per hour, the equation to find the time (h) is 4 = 3h. Solving gives h = 4/3 hours, or 1 hour and 20 minutes.

Write a sentence for the formula. Then interpret the equation in the context of the situation. "The formula d = rt relates the distance traveled d, the rate of travel r, and the time spent traveling t"

Answer explanation

The formula d = rt means that the distance (d) traveled is equal to the rate (r) multiplied by the time (t) spent traveling. For example, if you travel at 60 miles per hour for 2 hours, you cover 120 miles.