Mathematics
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Fluency · Pack B

8.8 Equations

Answer each question. Show working where needed.

Bronze

  1. Solve $7x = 56$.

  2. Solve $x + -3 = 12$.

  3. Solve $x - 12 = -3$.

  4. Solve $\dfrac{x}{6} = 5$.

  5. A function machine: $x \to \times 3 \to + 4 \to $ output. If output is 19, find $x$.

  6. Solve $4x + -3 = 13$.

  7. Solve $25 - x = 8$.

  8. Check whether $x = 5$ is a solution to $2x + 3 = 13$.

  9. Solve $-x = -8$.

  10. Solve $-3x = 12$ where $rhs$ may be negative.

Silver

  1. Solve $5x + -4 = 21$.

  2. Solve $4(x + -5) = 28$.

  3. Solve $7x - 3 = 3x + 17$.

  4. Solve $\dfrac{x}{5} + -1 = 4$.

  5. Solve $7(x - 2) = 21$.

  6. Solve $\dfrac{3x + -1}{4} = 5$.

  7. A kite has two pairs of sides $(2n + 1)$ cm and $(3n - 2)$ cm. The perimeter is 28 cm. Find $n$.

  8. Solve $5x + 12 = -3$ when $c$ is negative.

  9. I think of a number. I multiply by 4 and add 6. The result is 30. What is my number?

  10. A rectangle has length $(x + 5)$ and width $(x - 1)$. Its perimeter is 28 cm. Find $x$.

Gold

  1. Solve $\dfrac{5x - 2}{3} = 11$.

  2. Solve $5(x - 2) = 3(6 + x)$.

  3. Solve $\dfrac{x}{3} - \dfrac{x}{4} = 2$.

  4. Pete has 3 times as many songs as Sabrina, who has 120 fewer than Elena. If Pete has 360 songs, how many does Elena have?

  5. A student won 300 of 500 games, then won the next $x$ games. He has now won 80% overall. Find $x$.

  6. Three consecutive integers sum to $120$. Find them.

  7. Two angles in a triangle are $(2x + 10)°$ and $(3x - 20)°$, and the third is $90°$. Find $x$.

  8. A square has perimeter $4(x + 3)$ cm. Find $x$ when the perimeter is 32 cm.

  9. Solve $5x + 6 = 3x - 4$ where this gives a negative solution.

  10. I think of a number. I double it and add 5. I then triple the result and subtract 2. The result is 28. Find my number.

Platinum

  1. Solve $\dfrac{x + 1}{2} = \dfrac{x - 3}{5}$.

  2. Solve $\dfrac{2x + 1}{3} = \dfrac{x - 2}{2}$.

  3. A laptop costs $x$ chf. The shop applies a 25% discount, then adds 7.7% VAT. The final price is 807.75 chf. Find $x$.

  4. Two pens and three pencils cost 4.50 chf. One pen and two pencils cost 2.70 chf. Find the cost of each item.

  5. A man is 4 times his son's age now. In 4 years he will be 3 times. Find their current ages.

  6. Solve $\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{3}{4}$.

  7. Two consecutive integers have a product of 132. Find them by setting up and solving an equation.

  8. A bottle holds 1.5 L of squash mix at concentration $x$% sugar. Adding 0.5 L of water reduces concentration to 9%. Find $x$.

  9. Solve $5 - 2(3x - 4) = 7x - (x + 1)$.

  10. A rectangle has length $(2x + 1)$ and width $x$. Its area equals its perimeter. Find $x$.