Answer:
Question 6: The cost of a chocolate bar is $1.20 and the cost of a box of gum is $0.75
Question 7: There were 7 students
Explanation:
Question 6:
We will be using system of equations which a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations intersect.
Our Variables:
- chocolate bar which will be represent as b in the equation
- box of gum which will be represent as g in the equation
Forming the equations:
Sally -
bought 2 chocolate bars (b)
bought 1 box of gum (g)
to a total of $3.15
so 2b + 1g = $3.15
Evans -
bought 1 chocolate bars (b)
bought 2 box of gum (1)
to a total of $2.70
so 1b + 2g = $2.70
Solving using substation:
2b + 1g = $3.15 we want to isolate b to input into the other equation
1b + 2g = $2.70
2b + 1g = $3.15 subtract 1g from both sides, divided both sides by 2
2b / 2 + 1g - 1g = $3.15 - 1g / 2
b = $3.15 - 1g / 2
Now substation b into the second equation
1b + 2g = $2.70 becomes 1($3.15 - 1g / 2) + 2g = $2.70
simplify,
$3.15 + 3g / 2 = $2.70 isolate g
$3.15 + 3g / 2 x 2 = $2.70 x 2 multiply both sides by 2
$3.15 + 3g = $5.40 subtract $3.15, divided by 3 from both sides
$3.15 - $3.15 + 3g / 3 = $5.40 - $3.15 / 3
g = $5.40 - $3.15 / 3
g = $2.25 / 3
g = $0.75
Now plug in g to get b into any equation:
If Sally equation is used
2b + 1g = $3.15
2b + 1(0.75) = $3.15 → 2b + 0.75 = $3.15
2b + 0.75 - 0.75 = $3.15 - 0.75
2b = $2.40 → 2b / 2 = $2.40 / 2
b = $1.20
If Evans equation is used
1b + 2g = $2.70
1b + 2(0.75) = $2.70 → 1b + 1.50 = $2.70
1b + 1.50 - 1.50 = $2.70 - 1.50
1b / 1 = $1.20 / 1
b = $1.20
Question 7:
Our Variables:
- adult which will be represent as A in the equation
- student which will be represent as S in the equation
Forming the equations:
- sample size: group of 30
- Adult cost $5 (A)
- Student cost $2 (S)
- Five members are free
to a total cost is $104
so A + S = 30 - 5
this is how many of each variable from the total group and we subtract 5 as 5 members were free
so 5A + 2S = $104
Solving using substation:
A + S = 25 we want to isolate a to input into the other equation
5A + 2S = $104
a = 18
s =7