could you please help me with this math word problem,it is driving me insane.?

Question

at a football game, 200 souvenirs were sold, some at $1.50 each and the rest at $2.50 each.if the proceeds from the sales totaled $380, how many of each kind were sold?Let x represent the number of $1.50 souvenirs.

Answer 1

x = number of $1.50 souvenirs.

Since there is 200 souvenirs total, then the number of $2.50 souvenirs is (200 - x)

(Cost of Souvenir)(number sold) + (cost)(number sold) = total

(1.50)x + (2.50)(200 - x) = 380
1.50x + 500 - 2.50x = 380
-x = -120
x = 120

So, there are 120 of the $1.50 and 80 of the $2.50

Answer 2

Let x represent the number of souvenirs sold for $1.50. Then 200-x is the number of souvenirs sold for $2.50. The total proceeds are $380, so

$1.50x + $2.50(200-x) = $380

$1.50x + $500 - $2.50x = $380

$500 - $380 = $1.00x

x = 120.

To check our answer, 120 souvenirs sold for $1.50 gives us 120*1.50 = $180.

200-x = 200-120 = 80 sold at $2.50 each. That gives 80*$2.50 = $200.

$180 + $200 = $380, which checks.

So, 120 were sold at $1.50, and 80 were sold at $2.50.

Answer 3

Let x represent the number of $1.50 souvenirs. so (200 – x) represent the number of $2.50 souvenirs.
Amount of sale of $ 1.5 = x × 1.5 = 1.5 x
Amount of sale of $ 2.5 = (200 – x) × 2.5 = 2.5 × 500 – 2.5 x
Total sale = 1.5 x + 500 – 2.5 x = 380
– x = 380 – 500 = – 120
x = 120 tickets of $ 1.5
and (200 – 120) = 80 of $ 2.5

Answer 4

Let x = number of $1.50 souvenirs
Let 200 - x = number of $2.50 souvenirs

Then 1.50x + 2.50(200-x) = 380

Distribute the 2.50 through the parentheses:
1.50x + 500 - 2.50x = 380

Add the x terms:
-x + 500 = 380

Simplify:
500 - 380 = x
120 = x

Therefore you sold:
120 of the $1.50 souvenirs
80 of the $2.50 souvenirs

As a double-check:
200 souvenirs were sold.
120 x $1.50 = $180
80 x $2.50 = $200
Total sales = $380 <-- check

Answer 5

Let x = number of $1.50 souvenirs
Let 200 - x = number of $2.50 souvenirs

As total money is 380 so the money earned from both should be equal to that
So
1.50x + 2.50(200-x) = 380

1.50x + 500 - 2.50x = 380
-x + 500 = 380
500 - 380 = x
120 = x

Answer 6

X + Y = 200 => x = 200-y
1.50x + 2.50Y = 380

1½x + 2½y = 380
1½(200-y) +2½y = 380
300 -1½y + 2½y = 380
1y = 380 - 300 = 80
x = 200 - 80 = 120

120 souvenirs @ $1.50
80 Souvenirs @ $2.50

Answer 7

Let x = number of $1.50 souveniers
... then
200 - x = number of $2.50 souveniers

... so

1.50 x + 2.50(200-x) = 380

... and you can do the rest yourself, can't you?

1.5 x + 500 - 2.5 x = 380
-x + 500 = 380
-x = -120
x = 120

Answer 8

if you let x = the $1.50 souveniers then let y = $2.50

so this has to mean that x+y=200

we also know that 1.5x+2.5y=380

no using simultaneous equations you need to eliminate either x or y, I'll eliminate x

x+y=200 [multiply by 1.5 so the same number of x's is got]
1.5x+2.5y=380

1.5x+1.5y=300 or 1.5x+2.5y=380
1.5x+2.5y=380 1.5x+1.5y=300
- ____________ [subtract]
y=80

now substitute

x+y=200
x+80=200
x=120

check: 120X$1.50 =$180 plus 80X$2.50 =$200 = $380 i.e. correct

ANS 120 $1.50 souvenirs and 80 $2.50 souveniers

Answer 9

80 at 2.50 and 120 at 1.50

Answer 10

150 1.50 and 50 2.50