Question

За арбуз массой 7 кг и дыню массой 5 кг заплатили 250 рублей .Сколько стоит 1 кг арбуза и 1 кг дыни,если арбуз массой 8 кг на 64 рубля дешевле дыни массой 4 кг.Помогите пожалуйста,очень прошу

Answer 1

Надо решать системой:
Пусть хр - стоит 1 кг арбуза, а ур - стоит 1кг дыни
/7х + 5у = 250,     /7х + 5у = 250,     /7х +5(16 + 2х) = 250,    
\4у - 8х = 64;        \у - 2х = 16;          \у = 16 + 2х;

/7х + 80 + 10х = 250,  /17х = 170,    /х = 10,
\у = 16 + 2х;                \у = 16 + 2х;  \у = 36.

1 кг арбуза стоит 10 р, а 1 кг дыни стоит 36р.

Answer 2

Calculation of the Cost per Kilogram

To calculate the cost per kilogram of the watermelon and the cantaloupe, we can set up a system of equations based on the given information.

Let's assume the cost per kilogram of the watermelon is x rubles, and the cost per kilogram of the cantaloupe is y rubles.

From the given information, we can form the following equations:

Equation 1: 7x + 5y = 250 (since the total cost of the watermelon and the cantaloupe is 250 rubles) Equation 2: 8x - 4y = 64 (since the watermelon weighing 8 kg is 64 rubles cheaper than the cantaloupe weighing 4 kg)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express x in terms of y:

7x = 250 - 5y x = (250 - 5y) / 7

Substituting this value of x into Equation 2, we get:

8((250 - 5y) / 7) - 4y = 64

Simplifying the equation:

(2000 - 40y) / 7 - 4y = 64 2000 - 40y - 28y = 448 -68y = 448 - 2000 -68y = -1552 y = -1552 / -68 y = 22

Now, substituting the value of y back into Equation 1 to find x:

7x + 5(22) = 250 7x + 110 = 250 7x = 250 - 110 7x = 140 x = 140 / 7 x = 20

Therefore, the cost per kilogram of the watermelon is 20 rubles and the cost per kilogram of the cantaloupe is 22 rubles.

Please note that the negative values obtained during the calculation were due to the assumption made in the calculation process and should be ignored.

Let me know if you need any further assistance!