Amount

[Guest]

During it's first week in business, a store sold 108 (total) apples and oranges.

Week 2- Five times the number of apples and three times the number of oranges were sold.

A total of 452 apples and oranges were sold for week 2.

Calculate number of (each) apples and oranges sold the first week.

[Guest]

Let x=apples and y=oranges sold in week1
x + y = 108
5x + 3y = 452
3x + 3y = 324
2x = 128
x = 64 apples in week1
y = 44 oranges in week1

[Guest]

"3x + 3y = 324"

Was the 3x subtracted also because the 3y was subtracted ? Also, how was 324 obtained ?

[Guest]

"3x + 3y = 324"

Corrected post:

Was x changed to 3x and subtracted because the 3y was subtracted ? Also, how was 324 obtained ?

[Guest]

We are using algebra to provide a solution.
and we are using simultaneous equations in particular.
In the question we are told 2 things about selling fruit on week1 and week2.
1......how many pieces were sold in week1.....108
2......how many times more of each fruit was sold in week2 also the total of fruit sold in week2......5 times apples and 3 times oranges and total of 452 fruit...apples+oranges.

So if we.... Let x=apples and y=oranges sold in week1

x + y = 108 .....this is what we are told for week1 ....eqn1

5x + 3y = 452 .....this is what we are told for week2 ....eqn2

These are 2 simultaneous equations and we have to find a value for x and y that satisfies both.
In any equation what is added or subtracted from/to one side must be done on the other to keep the equation balanced.
also if I multiply/divide one side by 3 I must do same to other side.

I notice I have a 3y in eqn2 ... So if I multiply eqn1 by 3 I will get..
3x + 3y = 324
and as 3x + 3y equals 324 I can subtract 3x + 3y from the LHS and 324 from the RHS of eqn2 and things are still balanced.
This is called solution by elimination ....multiply/divide to get some term equal then subtract to eliminate....

This gives me .....
2x = 128
so dividing by 2 gives ...

x = 64 apples in week1

and x + y = 108 so y = 108 - 64 = 44
so
y = 44 oranges in week1

[Guest]

Thanks. I could not remember the procedure.