Help Math word problem!?

Question

At its grand opening, the Guthrie Market distributed two different types of souvenirs. One type costs 20 cents each, and the other type costs 25 cents each. One thousand souvenirs were distributed in all. If the cost of these souvenirs was $220, how many of each type were distributed?

Just can't figure this one out, Step-by-Step please!

Answer 1

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Answer 2

Call the number of the 25c souveneir X and the number of the 20c one Y. You're told that X + Y = 1000, and that 0.25X + 0.2Y = 220.

Now, if X + Y = 1000, then X = 1000 - Y. Plug that into the other equation: 0.25(1000 - Y) + 0.2Y = 220.

Now multiply out the parentheses: 250 - 0.25Y + 0.2Y = 220.

That simplifies to 250 - 0.05Y = 220. Subtract 220 and add 0.05Y to each side, and you get 30 = 0.05Y.

Now divide both sides by 0.05, which is the same as multiplying them by 20: 600 = Y.

Therefore, 600 of the cheaper souveneirs were sold. Since 1000 were sold in all, that makes 400 of the expensive ones.

To test this result, find the cost of the souveneirs. 600 * 20c = 12000c = $120. 400 * 25c = 10000c = $100. $100 + $120 = $220, so the answer is right.

600 of the 20c souveniers and 400 of the 25c ones were distributed.

Answer 3

Okay, so let's say the number of souvenirs distributed of type 1 is A, and the number of type 2 is B.

we have A + B = 1000
and
0.20A + 0.25B = 220
converting to fractions
A / 5 + B / 4 = 220
multiply by 20 to get rid of the fractions
4A + 5B = 4400

now back to the original A + B = 1000
A = 1000 - B
4A = 4000 - 4B
substitute in
4000 - 4B + 5B = 4400
4000 + B = 4400
B = 400
therefore A = 600

Answer 4

This is an exercise to convert words into symbols. Let's see what are your known and unknown values.

Known:
One type of souvenir cost 20cents.
The other costs 25cents.
One thousand souvenirs total.
Total cost is $220.

Unkown:
The number of souvenir 1.
The number of souvenir 2.

Let a variable stand for each type of souvenir. Let x be the number of souvenir 1 and y be the number of souvenir 2.

Now rewrite all the information you know in symbols.

x+y=1000 (total number of souvenirs is 1000)
0.20x+0.25y=220 (The price of souvenir 1 times its quantity is the total cost of all souvenir 1's. Likewise for souvenir 2. Their sum is 220).

Now you have two equations and two variables so you can solve them like normal.

Answer 5

Raj is right... But the real world can be different... Did anyone use a "souvenir-sharing" program to unlawfully obtain a souvenir without paying? So that, for instance, of 1000 distributed, 245 were distributed through limewire and the balance through Itunes...

Answer 6

You have two unknowns and need to find two equations.

You know the price of each type and the total, so if x is the number of type A and y is the number of type B, then
0.20X + 0.25Y = $220

Also, you know that there are 1000 total, so:
X+Y = 1000

solve the second equation for X. X = 1000-Y

replace X in the first equation and solve for Y. Subtract Y from 1000 to get X.

Answer 7

let the souvenirs be x and y
theequations
x+y=1000
20x+25y=22000
dividing by 5
4x+5y=4400
4x+4y=4000 (1)*4
subtracting y=400
substituting x=600
so 600 of 20c and 400 of 25c were distributed

Answer 8

Let x represent the 20 cent one and x+5 the 25 cent one...

220 dollars is the same as 22000 cents so...

22000= x + (5+x)

22000-5= 2x

21995=2x

x=10997.5 / .20 cents = 54987.5
x+5= 11002.5 / .25 cents = 44010

So therefore 54987.5 of the 20 cent one was sold and 44010 of the 25 cent one was sold