Question

Дві іграшки мали однакову ціну. Потім одна з них подешевшала на 5%, а друга на 10%. Після цього різниця в ціні іграшок стала 4 гр. Якою стала ціна дешевшої іграшки ?

Answer 1

X-y=0
0,95x-0,9y=4

-0,9x+0,9y=0
0,95x-0,9y=4

0,05x=4
x-y=0

x=80
y=80

Y подешевела на 10%, значит стала стоить 72 гр.

Answer 2

Problem Analysis

We are given two toys that initially had the same price. One of the toys decreased in price by 5%, while the other decreased by 10%. After these price reductions, the difference in price between the two toys is 4 gryvnias. We need to determine the new price of the cheaper toy.

Solution

Let's assume the initial price of each toy is P gryvnias.

After the first toy's price reduction of 5%, its new price will be P - 0.05P = 0.95P gryvnias.

After the second toy's price reduction of 10%, its new price will be P - 0.10P = 0.90P gryvnias.

The difference in price between the two toys is given as 4 gryvnias. Therefore, we can set up the following equation:

(0.95P) - (0.90P) = 4

Simplifying the equation:

0.05P = 4

Dividing both sides of the equation by 0.05:

P = 4 / 0.05 = 80

Therefore, the initial price of each toy was 80 gryvnias.

To find the new price of the cheaper toy, we can substitute the initial price into the equation:

New price of the cheaper toy = 0.95P = 0.95 * 80 = 76 gryvnias

So, the new price of the cheaper toy is 76 gryvnias.

Answer

The new price of the cheaper toy is 76 gryvnias.