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Maths problem in simultaneous equations

Maths problem in simultaneous equations-example-1
User Katie Byers
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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

User Ameeta
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