Answers to 2017 "Algebra" Problems -- page 1

Note: this is for a group of Students in Minneapolis MN preparing for the 6th grade math challenge. It is not for the general public.

Question #1. Maria and Juan collect coins -- you have the details.

J = 25:  M = 44-25 = 19

Mgold = 19 - 8 = 11  ;  Jgold = 15 - 11 = 4 (answer)

Question #6 Julio starts a savings account -- you have the details.

let M = months.

J = 100 + 50 M   Maria = 1000 + 25 M

100 + 50 M = 1000 +25M   subtract 25 M from both ises and subtract 100 from both sides:

25 M = 900 M = 36 (answer)  Check: 100 +50 times 36 = 1900 and 1000 + 25 times 36 = 1900

Question #4: Ivy thought of a number -- you have the details.

let x be the number:

(2x - 6) divided by 2 = x - 3 : (x  - 3) times 10 + 70 =  10x + 40

10x + 40  divided by 5 = 2x + 8 = 28 solve for x, x = 10 (Answer)

Check: various stages  10 20 14 7 70 + 70 = 140 28

Question # 7  Two acute angles of a triangle are in the ratio 3:2   What are the measures of the two angles.

This is a ratio and sum problem that a student named Kai Alton had a trick for.

Guess any two angles with the correct ratio: for example, 20 and 30. Add them up and get 50.

But we are supposed to get 90. 90 divided by 50 is 1.8.

Multiply each number by 1.8 and get 36 and 54 which are in the right ratio and add up to 90.

Note: 36 is 2 times 18 and 54 is 3 times 18. 36 degrees and 54 degrees (Answer).