If 8 jump ropes and 4 dolls cost $64, and 4 jump ropes and 8 dolls cost $92, how much will 12 jump ropes and 12 dolls cost?
what i dont get it
What, I don't get. Why does that equal 12 jumping ropes instead of dolls?
To solve this question, we can set up a system of equations to represent the given information. Let's assume the cost of one jump rope is "j" dollars and the cost of one doll is "d" dollars.
According to the first statement, 8 jump ropes and 4 dolls cost $64. This can be written as:
8j + 4d = 64
According to the second statement, 4 jump ropes and 8 dolls cost $92. This can be written as:
4j + 8d = 92
Now we have a system of two equations. We need to solve this system to find the values of "j" and "d" so that we can determine the cost of 12 jump ropes and 12 dolls.
To solve the system, we can use a method called substitution or elimination. I will use the substitution method.
From the first equation, we can isolate the value of "j":
8j = 64 - 4d
j = (64 - 4d) / 8
j = 8 - 0.5d
Now we substitute this value of "j" into the second equation:
4(8 - 0.5d) + 8d = 92
32 - 2d + 8d = 92
6d = 60
d = 10
Now that we have the value of "d", we can substitute it back into the first equation to find the value of "j":
j = 8 - 0.5(10)
j = 3
So, the cost of one jump rope is $3 and the cost of one doll is $10.
To find out the cost of 12 jump ropes and 12 dolls, we multiply the cost of one jump rope by 12 and the cost of one doll by 12, then add them together:
Cost of 12 jump ropes = 12 * 3 = $36
Cost of 12 dolls = 12 * 10 = $120
Therefore, the total cost of 12 jump ropes and 12 dolls is $36 + $120 = $156.
Thanks a lot it was great!
thanks damon
thanks a lot it really helped my son
8 j + 4 d = 64
4 j + 8 d = 92
multiply first eqn by 2
16 j + 8 d = 128
4 j + 8 d = 92
--------------- subtract
12 j = 36
j - 3 dollars per jump rope
then
d = 10 dollars per doll
You can do it now