On his farm, Mr. Mathews has goats and sheep in the ratio of 5:7. He decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. How much money does he make from the sale of the animals if the total number of sheep and goats on the farm is 360?
The total ratio of goats and sheep on the farm is 5+7 = 
<gadget id="calculator">5+7</gadget>
<output>12</output>
12.
The fraction that represents goats from the total ratio is 5/12, and since there are 360 goats and sheep on the farm, the number of goats is 5/12*360= 
<gadget id="calculator">5/12*360</gadget>
<output>150</output>
150.
The number of sheep on Mr. Mathews's farm is 360-150 = 
<gadget id="calculator">360-150</gadget>
<output>210</output>
210.
Mr. Mathews sold 1/2*150 = 
<gadget id="calculator">1/2*150</gadget>
<output>75</output>
75 goats.
If each goat went for $40, the total amount of money Mr. Mathews made from the sale of his goats is 75*$40 = $
<gadget id="calculator">75*40</gadget>
<output>3_000</output>
3000.
He also sold 2/3*210 = 
<gadget id="calculator">2/3*210</gadget>
<output>140</output>
140 of the total sheep on his farm.
The income from the sale of the sheep is 140*$30=$
<gadget id="calculator">140*30</gadget>
<output>4_200</output>
4200.
From the sale of goats and sheep, Mr. Mathews made $4200+$3000 = $8600.

<result>7_200</result>