Rose Harrison and Clara Huizink Solutions for Exercise 17: Mixed practice

Angles $x$ and $\frac{3}{4}\mathrm{x}$ are complementary. Find $x$. (Correct up to one decimal place)

The denominator of a fraction is $1$ less than twice the numerator. When $7$ is added to both the numerator and denominator, the resulting fraction is equivalent to$\frac{7}{10}$. Find the original fraction.

$x$ milligrams of a metal containing $45\%$ nickel must be combined with $6$ milligrams of pure nickel to form an alloy containing $78\%$ nickel. Find the value of $x$.

Chloe can type a story in $6$ hours. If Molly helps her, they finish typing the story in $4$ hours. Find how long it would take Molly to type the story on her own.

Mary takes $8$ days to do a full check of the library's online catalog. Her assistant takes $12$ days. If they work together, determine the fraction of the catalog that is checked after $4$ days.

The number of hamsters in a pet store doubles each month. Today, there are $20$ hamsters. Supposing that no hamster dies and no hamster gets sold, determine in how many months the store will have $640$ hamsters.

The number of hamsters in a pet store doubles each month. Today, there are $20$ hamsters. If $10$ hamsters are sold at the end of each month, after the number of hamsters double, find how many hamsters are left after $5$ months.

Sacha picked some apples from a tree in her garden. She then gave some to her friends. To her first friend, she gave half the apples she had, plus $2$ more. To her second friend, she gave half the apples she had left, plus $2$ more. And she did the same thing for her third friend. After giving away all these apples, she had $1$ apple left. Find how many apples she originally pick from the tree.