Question

Snap, Crackle and Pop went to the mall for shopping. They shopped in three different shops X, Y and Z. Snap bought two pairs of shoes, one belt and two pairs of pants at X. Crackle bought one pair of shoes, one belt, and four pairs of pants at Y. Pop bought two pairs of shoes, three belts, and one pair of pants at Z. The price of each pair of pants at shop Z was 20% more compared to other shops, while the belts and shoes were the same price across the stores.

They each spent the same amount of money - 2 500. What was the price of each belt?

Answer 1

Answer:

RS - 250

Step-by-step explanation:

hope it helps you

Answer 2

Answer:

156.25

Step-by-step explanation:

let price of  shoe be denoted as $h$, belt as $b$ and pants as $p$,

if Snap bought two pairs of shoes, one belt and two pairs of pants at X, then we can form the following equation;

$2h+b+2p=2500...............(1)$

If Crackle bought one pair of shoes, one belt, and four pairs of pants at Y, then;

$h+b+4p=2500...............(2)$

Pop bought two pairs of shoes, three belts, and one pair of pants at Z.

The price of each pair of pants at shop Z was 20% more compared to other shops, then the price of pants at shop Z is 1.2p

therefore;

$2h+3b+1.2p=2500...............(3)$

We solve for h, b and p in the three equations.

From eqn(1) we have that

$1b=2500-2p-2h$

We substitute this in eqn (2) and (3) to get

$1h+(2500-2p-2h)+4p=2500\\1h+2500-2p-2h+4p=2500\\-h+2p=0\\2p-h=0....................... (4)$

$2h+3(2500-2p-2h)+1.2p=2500\\2h+7500-6p-6h+1.2p=2500\\4.8p+4h=5000.........................(5)$

Now we solve for p and h in eqns (4) and (5)

from eqn (4)

$2p-h=0\\h=2p$

Substituting this value in eqn (5)

$4.8p+4(2p)=5000\\12.8p=5000\\p=390.625$

and

$h=2p\\h=2(390.625)\\h=781.25$

therefore;

$b=2500-2*390.625-2*781.25\\b=156.25$

The price of each belt is 156.25

$4.8p+4(2p)=5000\\12.8p=5000\\p=390.625$