Mathlete's Quiz 6 - Algebraic Reasoning (L-M)

Given -3 = n - 9, what is the value of n?

• -12

• -6

• 6

• 12

Answer explanation

To solve for n, add 9 to both sides of the equation: -3 + 9 = n, which simplifies to 6 = n. Therefore, the value of n is 6.

Francesca spent $56 at the grocery store. She had $24 after grocery shopping. Write and solve an equation to determine how much money, m, Francesca had before she did her grocery shopping.

• m = 80

• m = 32

• m = 56

• m = 24

Answer explanation

Let m be the amount Francesca had before shopping. The equation is m - 56 = 24. Solving gives m = 80. Thus, Francesca had $80 before grocery shopping.

Answer explanation

To find the value of b, solve the equation b + 7 = -19. Subtract 7 from both sides: b = -19 - 7, which simplifies to b = -26. Thus, the correct answer is b = -26.

Thomas and his three friends split a pizza. Each friend eats 5 pieces. Write and solve a division equation to determine how many pieces were in the whole pizza. Which division problem shows the number of pieces, p, in the pizza?

Answer explanation

Thomas and his 3 friends (4 people total) each eat 5 pieces. The equation \( \frac{p}{4} = 5 \) shows that the total pieces \( p \) equals 20. Thus, the correct choice is \( \frac{p}{4}=5 \) with \( p = 20 \).

One human year is equal to seven years in a dog’s life. Write and solve an equation to determine a dog’s age, a, in human years if it is 84 years old in dog years.

• 12 years

• 10 years

• 14 years

• 16 years

Answer explanation

To find the dog's age in human years, use the equation a = dog years / 7. For 84 dog years, a = 84 / 7 = 12. Thus, the dog's age in human years is 12 years.

• The value of m is -54.

• The value of m is 54.

• The value of m is -9.

• The value of m is 9.

Answer explanation

To find m, multiply both sides of \( \frac{m}{9} = -6 \) by 9. This gives \( m = -6 \times 9 = -54 \). Thus, the value of m is -54.

Determine the value of a in the equation 0.45 = 0.09a.

• 0.05

• 0.5

• 5

• 50

Answer explanation

To find a, divide both sides of the equation by 0.09: a = 0.45 / 0.09. Calculating this gives a = 5. Thus, the correct answer is 5.

Answer explanation

To solve for n, subtract \frac{2}{5} from 2\frac{9}{10}. Convert \frac{9}{10} to an improper fraction: 2\frac{9}{10} = \frac{29}{10}. Then, \frac{2}{5} = \frac{4}{10}. So, n = \frac{29}{10} - \frac{4}{10} = \frac{25}{10} = 2\frac{1}{2}.

Answer explanation

To solve \( \frac{5}{6}x = \frac{2}{3} \), multiply both sides by \( \frac{6}{5} \): \( x = \frac{2}{3} \cdot \frac{6}{5} = \frac{12}{15} = \frac{4}{5} \). Thus, the correct answer is \( x = \frac{4}{5} \).

Sara needs 56 quarts of chocolate milk to serve at her birthday party. She can only buy gallons of chocolate milk at her local grocery store. How many gallons will she need to buy?

• 4

• 14

• 56

• 224

Answer explanation

Sara needs 56 quarts of chocolate milk. Since 1 gallon equals 4 quarts, she divides 56 by 4, resulting in 14 gallons needed. Therefore, the correct answer is 14.