1819 C2X §9.5

• Wiskunde
• Middelbare school
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• Leerjaar 2

Which exercises should we discuss on the board?

Rearranging and substituting formulas

You can use the balance method to rearrange formules and to simplify formulas after using substitution. This is best explained with an example.

Rearranging formulas

Jake goes to a candy store. He wants to buy chocolate bars that cost 2 euros per bar and sour candies that cost 0.50 euro per candy. Jake wants to spend 12 euros.

We can describe the relation between the number of chocolate bars (c) and the number of sour candies (s) with the formula:

2c + 0.5s = 12

Rearranging formulas

We now have the formula 2c + 0.5s = 12

If Jake buys 3 chocolate bars, how many sour candies can he buy?

We can answer this question with an equation, fill in c = 3

2 x 3 + 0.5s = 12

6 + 0.5s = 12

0.5s = 6

s = 12

Jake can buy 12 sour candies.

Rearranging formulas

We can also rearrange  the formula 2c + 0.5s = 12 so we can directly calculate s if we know c.

2c + 0.5s = 12                  

    -2c               -2c

0.5s = 12 - 2c

 ÷0.5   ÷0.5  

s = 24 - 4c

So if Jake buys 3 chocolate bars: s = 24 - 4 x 3 = 12, he can buy 12 sour candies.

Rearranging formulas

When you rearrange  the formula 2c + 0.5s = 12

to s = 24 - 4c,

we say s is expressed in terms of c.

If you want to express c in terms of s, you would get:

2c + 0.5s = 12

2c = 12 - 0.5s

c = 6 - 0.25s

Rearrange the formula, express a in c:
5a - 10c = 40

Solution

5a - 10c = 40

5a = 40 + 10c

a = 8 + 2c

Substitution

Karen uses the following formula to decide how grams of sugar (s) she will need for her cake when she knows how many eggs (e) she uses:

s = 50e + 30

She also uses the following formula to know how many cupcakes (c) she can make, when she know how many grams of sugar she used:

c = 0.1s - 4

Substitution

We can combine these two formulas with substitution to directly calculate how many cakes we can make when we know the number of eggs.

s = 50e + 30                    c = 0.1s - 4

c = 0.1(50e + 30) - 4

c = 5e + 3 - 4

c = 5e -1

Substitute and simplify the result
y=3c+2 & c=-2a+4

Solution

y = 3c + 2                 c = -2a + 4

y = 3(-2a +4) + 2

y = -6a + 12 + 2

y = -6a + 14

HW Friday

Make and correct §9.5

Bring your workbook (for §9.6)