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I'm having difficulty solving this word problem. I just don't get it at all. I'm not too good with word problems. If anyone could help me; then that would be very helpful.

Simple calculator costs $\$5$ and scientific calculator costs $\$16$. The store sold $35$ calculators for total amount of $\$340$. How many of each calculator were sold?

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  • $\begingroup$ Just name $x$ the number of simple calculator and $y$ the number of scientific calculators which have been sold. So how many were sold and what was the amount of the total bill ? Try to do it and come back (if needed). $\endgroup$ – Claude Leibovici May 9 '15 at 15:52
  • $\begingroup$ The "routine" way is to let $x$ be the number of simple calculators sold, and $y$ the number of scientific calculators sold. We are told that $x+y=35$. We are also told that the total amount taken in was $340$, so $5x+16y=340$. Now use these two equations to find $x$ and $y$. $\endgroup$ – André Nicolas May 9 '15 at 15:52
  • $\begingroup$ @AndreNicolas Thank You $\endgroup$ – Larry May 9 '15 at 15:53
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Hint: start by asking what quantities you don't know and give them names. So you don't know "how many simple calculators" were sold and "how many scientific calculators" were sold. Give those quantities names, say $x$ is the number of simple calculators sold, and $y$ is the number of scientific calculators sold. Now, try to write the facts that you have as equations. The store sold 35 calculators total... so $x+y=35$. Each simple calculator sells for \$5, so the amount of money collected for selling simple calculators is $5x$. \$16 is collected for each scientific calculator sold, so the total from selling scientific calculators is $16y$. All together you collected \$340. This gives you an equation $5x+16y=340$.

Now, what is left is to solve two equations:

$$x+y=35$$ and $$5x+16y=340$$

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I did it a little differently.

5(35-X) + 16X = 340
175 - 5X + 16X = 340
175 + 11X = 340
11X = 165
X = 15
So 15 scientific and 20 regular calculators.

Or you could just as well approach it intuitively; for 16 you need a multiplier yielding a product ending in 0 and for 5 a multiplier yielding a product ending in 0 because there is no product of 16 which ends in ''5'' and the sum of the two products ends in ''0''. In the case of 5 there are only four possibilities less than 35 and 0 doesn't work

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