two groups of students went into the shop. the first group bought four hot dogs and six juices and paid $71. The second group bought three hot dogs and seven juices and paid $67. What were the prices for these items?
hot dog 9.5$ and juice 5.5$
hotdog 9.5 and juice 5.5
Could you possible show your workings?
To find the prices of hot dogs and juices, let's assign variables to them. Let's say the price of a hot dog is "H" and the price of a juice is "J".
Now, we have two sets of information:
First group (Group 1): 4 hot dogs and 6 juices for $71.
Second group (Group 2): 3 hot dogs and 7 juices for $67.
We can create two equations using this information:
Equation 1: 4H + 6J = 71
Equation 2: 3H + 7J = 67
To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method:
Multiply Equation 1 by 3 and Equation 2 by 4 to make the coefficients of "H" in both equations the same:
Equation 1: 12H + 18J = 213
Equation 2: 12H + 28J = 268
Now, subtract Equation 1 from Equation 2 to eliminate "H":
(12H + 28J) - (12H + 18J) = 268 - 213
12H - 12H + 28J - 18J = 55
10J = 55
J = 55 / 10
J = 5.5
Now substitute the value of J into Equation 1 or Equation 2:
4H + 6(5.5) = 71
4H + 33 = 71
4H = 71 - 33
4H = 38
H = 38 / 4
H = 9.5
Therefore, the price of a hot dog (H) is $9.50, and the price of a juice (J) is $5.50.