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A kid spent $100.00 to get 100 toy animals. The child bought at least one cat, one fish, and one bird, and did not buy any other toy animals. If a cat costs $10.00, a fish costs $3.00, and a bird costs $0.50, how many of each toy did the child buy?

Respuesta :

frika

Answer:

5 cats, 1 fish and 94 birds

Step-by-step explanation:

Let

  • c be the number of cats;
  • b be the number of birds;
  • f be the number of fish.

A kid bought 100 toy animals, then

[tex]c+b+f=100[/tex]

If a cat costs $10.00, then c cats cost $10c.

If a fish costs $3.00, then f fish cost $3f.

If a bird costs $0.50, then b birds cost $0.5b.

In total,

[tex]10c+3f+0.5b=100[/tex]

We get the system of two equations:

[tex]\left\{\begin{array}{l}c+b+f=100\\10c+3f+0.5b=100\end{array}\right.[/tex]

From the first equation:

[tex]b=100-c-f[/tex]

Substitute it into the second equation:

[tex]10c+3f+0.5(100-c-f)=100\\ \\10c+3f+50-0.5c-0.5f=100\\ \\9.5c+2.5f=50\\ \\95c+25f=500\\ \\19c+5f=100\\ \\f=20-\dfrac{19}{5}c[/tex]

Number f must be a whole number greater than 0, so

[tex]20-\dfrac{19}{5}c>0\\ \\c<\dfrac{100}{19}\\ \\c\le 5\dfrac{5}{19}[/tex]

Number c must be a multiple of 5, thus the only possible value for c is 5.

When c = 5, then

[tex]f=20-5\cdot \dfrac{19}{5}=20-19=1\\ \\b=100-5-1=94[/tex]

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