Natan spent $815 on sweaters and shirts. The number of shirts he bought was 1/2 the number of sweaters he bought. The cost of a shirt was $4 more than the cost of a sweater. He paid $245 more on sweaters than on shirts. Find the cost of 4 sweaters and 10 shirts.

Answer 1

Let's start by defining some variables.

Let x be the number of sweaters Natan bought.
Then, the number of shirts he bought is 1/2x.

Let y be the cost of a sweater.
Then, the cost of a shirt is y + 4.

We know that Natan spent $815, so:

yx + (y + 4)(1/2x) = 815

Simplifying this equation:

2yx + x(y + 4) = 1630

2yx + xy + 4x = 1630

3yx + 4x = 1630

We also know that Natan paid $245 more on sweaters than on shirts, so:

yx = (1/2x)(y + 4) + 245

Simplifying this equation:

2yx = yx + 2x + 490

yx = 2x + 490

Now we have a system of two equations:

3yx + 4x = 1630
yx = 2x + 490

We can solve for yx (the total cost of sweaters) by substituting the second equation into the first:

3(2x + 490) + 4x = 1630

6x + 1470 + 4x = 1630

10x = 160

x = 16

So Natan bought 16 sweaters and 8 shirts.

To find the cost of 4 sweaters and 10 shirts, we need to know the cost of one sweater and one shirt. We can use the equation yx = 2x + 490 to find y:

yx = 2x + 490

y(16) = 2(16) + 490

16y = 522

y = 32.63

So one sweater costs $32.63 and one shirt costs $36.63.

Therefore, 4 sweaters cost 4 * $32.63 = $130.52 and 10 shirts cost 10 * $36.63 = $366.30.