Question

can someone explain to me step by step how to do this question:

three pumps can transfer 4150 gal of water per day when working at the same time. Pumps A and B together can transfer 3200 gal per day. Pumps A and C together can transfer 2900 gal per day. How many gallons can each pump transfer working alone? Translate the equation and solve.

Answer 1

how much do A and B transfer in a day.
Can you write that as an equation?

Answer 2

x= pump A
y= pump B
z= pump C

x+y+z= 4150
x+y= 3200
x+z= 2900

i dont know what to do from here.

Answer 3

that is a good start. (Though I would have used A, B, C as the variables, why add to the confusion?)

Answer 4

We have 3 equations and 3 unknowns

I would use elimination.
write it as
1x+1y+1z= 4150
1x+1y+0z= 3200
1x+0y+1z= 2900

if we ignore for the moment the x,y,z
1 1 1 4150
1 1 0 3200
1 0 1 2900

Elimination means make the first column 1 0 0
now multiply the 1st row by -1 and add the result to the 2nd row
Can you do that?

Answer 5

z=950

Answer 6

1 1 1 4150 (mult by -1 to get -1 -1 -1 -4150.)
1 1 0 3200 add -1 -1 -1 -4150 to get 0 0 -1 -950
1 0 1 2900

the new problem is
1 1 1 4150
0 0 -1 -950
1 0 1 2900

to get rid of the 1 in the last row, do the same thing. mult the first row by -1 and add to the last row

1 1 1 4150
0 0 -1 -950
1 0 1 2900 add -1 -1 -1 -4150 to get 0 -1 0 -1250

we now have
1 1 1 4150
0 0 -1 -950
0 -1 0 -1250

if we add back the x,y,z this means
x+y+z= 4150
-z= -950
-y= -1250

Answer 7

x=1950

Answer 8

thank you. can you help me with another question?

Answer 9

Looks like you got the answers,

Post it.

Answer 10

The members of the graduating class at Grant High School arranged themselves in 8 rows with the same number of students in each row. When they rearranged themelves into 9 rows, they were 3 fewer members in each row than were before. How many members are there in the class?

Answer 11

make two equations.
x is the number of students in the 8 rows
x-3 is the number when they use 9 rows
y is total number of students

Answer 12

let me be clearer. x is the number of students in 1 row, when they assembled into 8 rows
so 8x= y

Answer 13

would the eqations be x-3=9 and 8x-y=0?

Answer 14

I was thinking
8x=y
9(x-3)= y

Answer 15

i dont understand.

the answers i can choose from are a)144 b)192 c)216 d)243 e)388

Answer 16

e)288*

Answer 17

if you have x people in 8 rows then you have 8x people

they then tell us
When they rearranged themelves into 9 rows, they were 3 fewer members in each row
so if there were x people in each row, now there are x-3 people in each row
the total number of people is 9(x-3)
if we call y the total number we have

8x=y
9(x-3)=y