Aquaman

Aquaman Kebule shopped at Captain Nemo's fishmonger, where the prices of all goods were listed in whole scales. If Kebule bought 2 crayfish, 3 clams, and 1 pike, he would pay 49 scales. If he bought 5 more crayfish, 11 clams, and 1 pike, he would pay a total of 154 scales. How many scales would he pay for 1 crayfish, 2 clams, and 3 pike?

Final Answer:

x₁ =  79
x₂ =  60

Step-by-step explanation:

$$\begin{gathered} 2a+3b+1c=49 \\ 49+5a+11b+1c=154 \\ {a}_1=8;b_1=4;c_1=21 \\ {a}_2=16;b_2=1;c_2=14 \\ {x}_1=1\cdot a_1+2\cdot b_1+3\cdot c_1=1\cdot 8+2\cdot 4+3\cdot 21=79 \end{gathered}$$

$$\begin{gathered} x_2=1\cdot a_2+2\cdot b_2+3\cdot c_2=1\cdot 16+2\cdot 1+3\cdot 14=60 \\ \text{ Verifying Solution: } \\ {w}_1=2\cdot a_1+3\cdot b_1+1\cdot c_1=2\cdot 8+3\cdot 4+1\cdot 21=49 \\ {w}_2=2\cdot a_2+3\cdot b_2+1\cdot c_2=2\cdot 16+3\cdot 1+1\cdot 14=49 \\ {w}_3=49+5\cdot a_1+11\cdot b_1+1\cdot c_1=49+5\cdot 8+11\cdot 4+1\cdot 21=154 \\ {w}_4=49+5\cdot a_2+11\cdot b_2+1\cdot c_2=49+5\cdot 16+11\cdot 1+1\cdot 14=154 \end{gathered}$$

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