Posted by Max on Wednesday, October 17, 2012 at 9:45am.
GB = 8*G
BB = 3*B
GB - BB = 46
Where GB is the number of girl's books, BB is the number of boy's books, G is the number of girls, and B is the number of boys.
Use algebra to solve this system of equations
2nd problem
B/G = 2/3
G(glasses) + G(noglasses) = G
G(glasses)/G(noglasses) = 1/3
G - B = 12
where B is number of boys, G is number of girls, G(glasses) is number of girls with glasses, G(noglasses) is number of girls without glasses
Use algebra to solve this system of equations
3rd question:
1.6 m = 160 cm; 1.47 m = 147 cm
(160 + 147 + x) / 3 = 150
where x is the height of the third girl. Solve for x
4th question
The water in the tank before the tap turns on is
2/5 * 40 * 20 * 20 = 3200 cm3 = 3.2 L
After three minutes, 2.5 * 3 = 7.5 L
The total amount of water in the tank is 3.2 L + 7.5 L
1. number of girls ---- x
number of boys --- 36-x
8x - 3(36-x) = 46
8x - 108 + 3x = 46
11x = 154
x = 14
There are 14 girls in the class
2. number of boys = 2x
number of girls = 3x
1/4 of the girls wear glasses, or
(3/4)x girls wear glasses
"there are 12 more girls than boys" ---> x - (36-x) = 12
2x = 48
x = 24
There are 24 girls , and 1/4 of those wear glasses
Then 6 girls wear glasses
check:
24 girls and 12 boys, ratio is 12:24 = 2:3 , checks
1/4 of the 24 girls wear glasses ---> 6 girls wear glasses
ratio of glassed girl to non-glassed girls = 6 : 18 = 1:3 , checks
All is good!
3. (x+1.6+1.47)/3 = 1.50
x+1.6+1.47 = 4.5
x = 1.43
Third girl is 1.43 m or 143 cm tall
4. rate of flow = 2.5 L/min
after 3 minutes new amount of water = 3(2.5) = 7.5 L
plus the (2/5)(40)(20)(20) or 6400 mc^3 or 6.4 L already in tank
gives us 13.91 L