Twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71. What are the numbers?
A The larger number is 14 and the smaller number is 5.
B The larger number is 17 and the smaller number is 8.
C The larger number is 20 and the smaller number is -3.
D The larger number is 12 and the smaller number is 7.
E The larger number is 24 and the smaller number is 8.
F The larger number is 8 and the smaller number is 7.
The number of girls at a small high school is 60 greater than the number of boys. If there are 1250 total students, how many girls are there?
A 625
B 705
C 635
D 655
E 725
F 675
2007-05-23 06:31:46 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A) 14 & 5
D) 655
2007-05-23 06:42:20 · answer #1 · answered by happycoloredmarbles 2 · 0⤊ 0⤋
A because 2*14 = 5*5+3 and 4*14 + 3*5 = 71
x = number of boys
x+60 = number of girls
2x+60 = 1250
2x = 1190
x = 595 = number of boys
x+60 =595+60 = 655 = number of girls
2007-05-23 07:03:25 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
Let s be the smaller number and l be the larger number
Then
2l = 5s + 3 and 4l + 3s = 71
Now they can be set up in a system of equations. I'll start by getting the variables all on one side (2l - 5s = 3) and multiplying it by -2 to cancel out with the other equation (-4l + 10s = -6)
Now add them together
4l + 3s = 71
-4l + 10s = -6
-------------------
0 + 13s = 65
divide by 13
s = 5
Plugging 5 back into the equations for s, I come up with
l = 14
so your answer is A
The total number of boys (x) plus the total number of girls (x + 60) equals 1250
x + (x + 60) = 1250
2x + 60 = 1250
2x = 1190
x = 595 (the number of boys)
x + 60 = 655, D the number of girls
2007-05-23 06:50:43 · answer #3 · answered by kamcrash 6 · 0⤊ 0⤋
First question is A. 2x-5y=3 and 4x+3y=71 x=larger Number and y=smaller number. Solve for y and you should get 5 and then plug it in to either equation and you should get 14.
Second question is D. Half the total students which is 625 then add 30 to it and you get 655
2007-05-23 06:53:55 · answer #4 · answered by Ronald C 2 · 0⤊ 0⤋
Anytime you have problems like this you want to extract the information and organize it into a system of equations:
1) call the larger number x and the smaller y
from the first sentence you know:
2x = 5y + 3
and from the second you know:
4x + 3y = 71
rewrite the first equation and get :
4x - 10y = 6
subtract it from the second equation and get:
13y = 65
y = 5
plug this back in to the first equation and get:
2x = 5(5) + 3
x = 14
Thus A is your answer.
2) let g be the number of girls, b the number of boys:
you know:
g - 60 = b
g + b = 1250
sub for b in the second equation to get:
2g - 60 = 1250
2g = 1310
g = 655
answer D
2007-05-23 06:43:23 · answer #5 · answered by emp211 3 · 0⤊ 0⤋
The first question is A. I basically used the answers to complete the question.
The second question is D. 1250-655=595, 655-595=60
2007-05-23 06:40:12 · answer #6 · answered by jigyarjan818 1 · 0⤊ 0⤋
1)2L=3+5S
2) 4L+3S=71
multiply eqn 1) times 2----4L=6+10S
insert into eqn 2
6+10S+3S=71
6+13S=71
13S=65
S=65/13=5
then
2L=3+5*5=28
L=14
2nd ?
G=60+B
G+B=1250
60+B+B=1250
2B=1190
B=595
G=595+60=655
2007-05-23 06:46:06 · answer #7 · answered by pinetreexl 1 · 0⤊ 0⤋
c and there is not a correct answer for the bottom one. it is 685
2007-05-23 06:39:52 · answer #8 · answered by Christina 3 · 0⤊ 1⤋
A, D
2007-05-23 06:43:31 · answer #9 · answered by sweetwater 7 · 0⤊ 0⤋
A , D
2007-05-23 06:40:33 · answer #10 · answered by jiang z 1 · 0⤊ 0⤋