+1090 These questions were on my Math UIL Test, and I wasn't sure how to solve them.
1. What is the area of a rhombus with diagnols that measure $${\mathtt{4}}$$$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ and 8 cm?
2. If 2x - 3y = 4 and x + y = 7, then x - y =
3. The population of Beaver Dome is 1/3 the population of Clairette. If Clairette has 5000 more people then Beaver Dome, then what is the population of Clairette?
4. At the youth church fundraiser, a cookie costs 10¢, a donut costs 25¢, and a sweet roll costs 30¢. If one wanted to get at least one of each of the items, how many different ways could one do this using exactly $1?
5. On a true-false test, Dan answered 15 of the first 20 problems correctly but only one third of the remaining problems correctly. If the final score was 50% correct, how many problems were on the test?
+23246 1) One of the formulas for the area of a rhomus is: A = ½·d1·d2, where d1 and d2 are the lengths of the rhombus. Area = ½·4.5·8 = 18
2) 2x - 3y = 4 ---> 2x - 3y = 4
x + y = 7 ---> multiply by 3 ---> 3x + 3y = 21
add down: 5x = 25 ---> x = 5 ---> y = 2
---> x - y = 5 - 2 = 3
3) B = (1/3)·C
C = 5000 + B ---> C = 5000 + (1/3)·C ---> (2/3)·C = 5000 ---> C = 7500
4) I don't have a neat way of doing this:
10C + 25D + 30R = 100 seven ways:
C = 10, D = 0, R = 1
C = 7, D = 0, R = 1
C = 5, D = 2, R = 0
C = 4, D = 0, R = 2
C = 2, D = 2, R = 1
C = 1, D = 0, R = 3
C = 0, D = 4, R = 0
5) Let x be the number of questions after the first 20:
This equations represents the number of correct answers:
15 + (1/3)x = (1/2)(x + 20)
Multiply by 60:
900 + 20x = 30(x + 20)
900 + 20x = 30x + 600
300 = 10x
x = 30 (extra questions)
Total number of questions: 20 + 30 = 50
+23246 1) One of the formulas for the area of a rhomus is: A = ½·d1·d2, where d1 and d2 are the lengths of the rhombus. Area = ½·4.5·8 = 18
2) 2x - 3y = 4 ---> 2x - 3y = 4
x + y = 7 ---> multiply by 3 ---> 3x + 3y = 21
add down: 5x = 25 ---> x = 5 ---> y = 2
---> x - y = 5 - 2 = 3
3) B = (1/3)·C
C = 5000 + B ---> C = 5000 + (1/3)·C ---> (2/3)·C = 5000 ---> C = 7500
4) I don't have a neat way of doing this:
10C + 25D + 30R = 100 seven ways:
C = 10, D = 0, R = 1
C = 7, D = 0, R = 1
C = 5, D = 2, R = 0
C = 4, D = 0, R = 2
C = 2, D = 2, R = 1
C = 1, D = 0, R = 3
C = 0, D = 4, R = 0
5) Let x be the number of questions after the first 20:
This equations represents the number of correct answers:
15 + (1/3)x = (1/2)(x + 20)
Multiply by 60:
900 + 20x = 30(x + 20)
900 + 20x = 30x + 600
300 = 10x
x = 30 (extra questions)
Total number of questions: 20 + 30 = 50
