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.
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.