# A woman buys toys worth 2490 which include dolls worth 29 each and balls worth 33 each. How of each did she buy.

justaguide | Certified Educator

The woman bought toys worth 2490 which included dolls worth 29 each and balls worth 33 each.

Let the number of dolls bought be D and the number of balls bought be B. Both B and D have to be integers.

33*B +29*D = 2490

Using trial and error the equation holds for B = 28 and D = 54

The woman bought 28 balls and 54 dolls

vaaruni | Student

Cost of 1 set of Art-kit + 1 set of Tool-kit = 33 + 29 = 62\$

Total Amount = 2490\$

Let us assumed equal number (x) of each kind of toys has been purchased,

Then  29x + 33x = 2490,

=>62x = 2490  => x = 2490/62 =>  x = 40  and  Remainder(R)= 10

Here the remainder(R=10) indicates that one of the item should be > 40 and the  other kind < 40.

The difference in prices of two kinds of toys à 33-29=4 shows that

on increasing one kind of item(Tool-kit) by 1 and decreasing the other kind(Art-kit) we  save 4\$.

Therefore on decreasing No. of Art-kit by 12 and increasing the other toy   (Tool-kit) by the same number (12) we save 4*12=48\$ and adding the remaining 10\$   the total savings becomes 48+10 = 58\$ and with 58\$, two(2) more Too-kit(29\$ each)  could be bought.

This makes number of Tool-kit bought = 40+12+2 = 54 and the

Number of Art-kit set bought = 40 – 12 = 28

Number of Art-kit set = 28  and  Number of Tool-kit = 54

She bought 28 set of Art-kit and  54 set of tool-kit <-- Answer