Lily bought blue toys for $ 7 each and red toys for $ 5 each. She spent a toal amount of $ 104.
How many of each kind of toys did she buy?
2007-12-13 10:41:28 · 14 answers · asked by I N 2 in Science & Mathematics ➔ Mathematics
The total toys bought is unknown.
2007-12-13 10:42:14 · update #1
How did you get it?
2007-12-13 10:45:23 · update #2
This is an open question. There are several possible answeres.
It could be 12 blue 4 red or 7 blue 11 red or 2 blue and 18 red.
How you get it is do the blue's first and multiply until you can get a remainder of 4. Just trial and error.
7*1=7 104-7=97 97 cant divide by 5 NO Good
7*2=14 104-14=90 90 divided by 5= 18 GOOD
and so on
2007-12-13 10:56:11 · answer #1 · answered by Hotdawgy 2 · 0⤊ 0⤋
OK
7x + 5y = 104
7x = 104 -5y
x = 104-5y /7
So 104-5y must be divisible by 7
If y is 1,2 or3, the result is NOT an integer.
When y = 4 , the result is 12.
SO let's check
7(12) + 5(4) = 104?
84 + 20 = 104?
104 = 104 YES!!
So 12 blue and 4 red is one answer.
At y =5,6,7,8,9 the result is NOT an integer.
At y = 11, the result is 7
So let's try it
7(7) + 5(11) = 104??
49 + 55 = 104
104 = 104 YES!!
So 7 blue and 11 red is also an answer.
At y = 10,11,12,13,14,15,16,17 the result is NOT an integer.
At y = 18, the result is 2
7(2) + 5(18) = 104??
14 + 90 = 104??
104 = 104 YES
So 2 blue and 18 red is also an answer.
So you have three possible answers
12 blue and 4 red
7 blue and 11 red
2 blue and 18 red
All three work based upon the information.
Hope that helps.
2007-12-13 19:00:33 · answer #2 · answered by pyz01 7 · 1⤊ 0⤋
An answer is immediately obvious because after accounting for the number of $7 toys, you must be left with an amount that is evenly divisible by 5, i.e., it must end in a 5 or a 0
Since the original amount ends in a 4, and we know that 7*2 = 14, then when we subtract 14 from 104, we'll end up with a number divisible by 5
2 blue, 18 red
2007-12-13 18:46:35 · answer #3 · answered by dogsafire 7 · 0⤊ 0⤋
2 blue and 18 red
or
7 blue and 11 red
or
12 blue and 4 red
7b + 5r = 104
r = -7b/5 + 104/5
only when b = 2, 7 or 12 (5 apart) will the values of r be whole numbers. And since you can't buy "part" of a toy....
2007-12-13 18:49:42 · answer #4 · answered by Linda K 5 · 0⤊ 0⤋
k, so x is # of red and y # of blue
7y+5x=104
since there is no other info, we need to guess and check
x=1
7y+5=104
7y=104-5=101
101 is not divisible by 7, so this cannot be a solution
x=2
7y+10=104
7y=94
nope
x=3
7y+15=104
7y=89
nope
x=4
7y+20=104
7y=84
y=12
thus one possible way is 12 blue and 4 red
x=5
7y+25=104
7y=79
nope
x=6
7y+30=104
7y=74
nope
as u can see, the pattern for 7y is -5 each time
thus, the next answers are
69
64
59
54
49
44
39
34
29
24
19
14
9
4
the next are negatives, so don't even go there, its useless
the only ones divisible by 7 are 49 and 14. so y=7 and y=2 in that order
y=12, x=4
y=7, x=11
y=2, x=18
2007-12-13 18:58:18 · answer #5 · answered by Harris 6 · 0⤊ 1⤋
12 blue toys 4 red
2007-12-13 18:44:37 · answer #6 · answered by BrockyB 2 · 0⤊ 0⤋
18 times 5 = 90
7 times 2 = 14
90=14=104
18 red toys and 2 blue toys
2007-12-13 18:48:30 · answer #7 · answered by Lady Lefty 3 · 0⤊ 1⤋
11 red and 7 blue.
11 times 5=55
7times 7=49
49+55=104 :)
2007-12-13 18:46:06 · answer #8 · answered by modelgirl_x 2 · 0⤊ 0⤋
So 7x + 5y = 104, and we want integral solutions for x and y. Note that
5y = 104 - 7x
In other words, 104-7x is divisible by 5. This occurs for x = 2.
2 blue toys, 18 red toys.
Of course, this isn't the only solution. (7,11) and (12,4) also work.
2007-12-13 18:46:52 · answer #9 · answered by Anonymous · 0⤊ 0⤋
12 blue toys and 4 red toys - You get the answer by trial and error.
2007-12-13 18:50:05 · answer #10 · answered by A.N. 2 · 0⤊ 0⤋