Four people, A, B, C, and D, go shopping. When paying the bill, each of them takes out some money. It is known that the sum of the three people’s payment is 5 times that of A, and the sum of the payment of A, C, and D is 4 times that of B. A, B, and D The sum of the three people's payment is three times that of C, and D paid 46 yuan, so how much did the four people spend in total?
甲乙丙丁四个人去购物，付账时每人都拿出一些钱，已知，乙丙丁三人付钱的总和是甲的5倍，甲丙丁三人付钱的总和是乙的4倍，甲乙丁三人付钱的总和是丙的3倍，丁付了46元，那么四个人共花了多少元．
<gadget id="calculator">1 + 5</gadget>
<output>6</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 + 4</gadget>
<output>5</output>

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 + 3</gadget>
<output>4</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 - (1/6) - (1/5) - (1/4)</gadget>
<output>23/60 = around 0.383333</output>

<gadget id="calculator">46 / (23/60)</gadget>
<output>120</output>

<result>120</result>