Apples and pears

Apples cost 50 cents piece, pears 60 cents piece, bananas cheaper than pears. Grandma bought 5 pieces of fruit. There was only one banana, and I paid 2 euros 75 cents. How many apples and how many pears?

Correct answer:

j₁ =  0
h₁ =  4
j₂ =  1
h₂ =  3
j₃ =  2
h₃ =  2

Step-by-step explanation:

$$\begin{gathered} 50j+60h+b\cdot 1=275 \\ j+h+1=5 \\ b<60 \\ j>=0 \\ {b}_1=35,h_1=4,j_1=0 \\ {b}_2=45,h_2=3,j_2=1 \\ {b}_3=55,h_3=2,j_3=2 \\ {j}_1=0=0 \end{gathered}$$

$h_1=5-1-j_1=5-1-0=4$

$j_2=1=1$

$h_2=5-1-j_2=5-1-1=3$

$j_3=2=2$

$h_3=5-1-j_3=5-1-2=2$

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