Question

Andy and alex order prints andy orders 40 small and 10 large for 32.50 and alex orders 20 small and 8 large for 20. How much does small and large prints cost

Answer 1

Answer:

Unit price of small prints=y=0.5

Unit price of large prints=x=1.25

Step-by-step explanation:

Let the price for each unit of large prints be x, and the price of each unit of the small prints be y.

Andy orders 40 small prints each at a unit price of y,this can be expressed as 40×y=40y, he also orders 10 large prints each at a unit price of x, this can be expressed as 10×x=10x.

The total amount the Andy spends on all prints=Total he spends on small prints +Total he spends on large prints

Where the Total he spends on all prints=32.50

Total he spends on small prints=40y

Total he spends on large prints=10x

Replacing;

10x+40y=32.50    ...Equation 1

Alex on the other hand orders 20 small prints each at a unit price of y,this can be expressed as 20×y=20y, he also orders 8 large prints each at a unit price of x, this can be expressed as 8×x=8x.

The total amount the Alex spends on all prints=Total he spends on small prints +Total he spends on large prints

Where the Total he spends on all prints=20

Total he spends on small prints=20y

Total he spends on large prints=8x

Replacing;

8x+20y=20    ...Equation 2

Combining equation 1 and 2 and solving:

4(10x+40y=32.50) >>>>>>>40x+160y=130

5(8x+20y=20) >>>>>>>>     40x+100y=100  

Subtract equation 2 from 1 (40x-40x)+(160y-100y)=(130-100)

60y/60=30/60

y=0.5

Replacing the value of y in equation 2, 8x+20y=20

8x+(20×0.5)=20

8x+10=20

8x/8=10/8

x=1.25

Unit price of small prints=y=0.5

Unit price of large prints=x=1.25