Proportional Reasoning and Number Theory As a rough guide, use half a page to explain how to solve each problem, including any diagrams (assuming single-space formatting). There are 6 problems, so...

Proportional Reasoning and Number Theory

As a rough guide, use half a page to explain how to solve each problem, including any diagrams (assuming single-space formatting). There are 6 problems, so your entire document should be approximately 3 pages.
A museum contained an equal number of indigenous masks and weavings. After 6 masks and 10 weavings were loaned to a traveling exhibition, the ratio of remaining masks to weavings was 7 to 5. How many masks and weavings were there initially? [Hint: Use a strip diagram.]
Tina is going to paint different parts of a totem pole with a mixture of green paint and blue paint. She mixes 34 of a cup of green paint with 23 of a cup of blue paint to get the right colour. She will need 34 cups of paint in total. How many cups of green paint and how many cups of blue paint will she need? [Hint: Use ratios.]
Hugo is comparing two different investments. For investment A he has to pay a management fee of 2% per year, but he will earn interest of 5% per year (on the invested amount after taking out the 2% management fee). For investment B there is no management fee, but he will earn interest of 3% per year. Which of the two investments should he choose? Or are they both equivalent? [Hint: To decrease a number by 1%, for example, multiply the number by 1 – 0.01 = 0.99, but to increase a number by 1%, multiply the number by 1 + 0.01 = 1.01.]
Yolanda has a collection of 3,689 beads. In how many different ways can Yolanda arrange her bead collection into groups so that the same number of beads are in each group and so that there are no beads left over (i.e., not in a group)? [Hint: Use either factors or multiples.]
Explain how to determine whether the number 111,222,333,444,555,666,777,888,999,000 is divisible by 6 without using a calculator or doing long division. [Hint: 6 = 2 x 3.]
A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM.]