Jonathan and members of his Spanish Club are going to Costa Rica. He purchases 10 traveler's checks in denominations of $20, and $100, totaling $370. He has twice as many $20 checks as $50 checks. How many of each denomination does he have?

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Answer 1 · 2016-10-23T03:16:58

Let the no. of $50 checks be x

then the no. of $20 checks would be 2x

and the no. of $100 checks would be 10-x-2x=10-3x

Total amount being $370 we can write

$2 x \times $ 20 + x \times $ 50 + (10 - 3 x) \times $ 100 = $ 370$ $2x xx$20+x xx$50+(10-3x)xx$100=$370$

$\Rightarrow 40 x + 50 x + 1000 - 300 x = 370$ $=>40x+50x+1000-300x=370$

$\Rightarrow - 210 x = 370 - 1000 = - 630$ $=>-210x=370-1000=-630$

$\Rightarrow x = \frac{630}{210} = 3$ $=>x=630/210=3$

So denomination is as follows

The no. of $50 checks = $3$ $3$

The no. of $20 checks $= 6$ $=6$

The no. of $100 checks $= 10 - 3 \cdot 3 = 1$ $=10-3*3=1$