# Math Help - formula please?

1. ## formula please?

3 rabbits cost £19.70
the second rabbitt cost £2 more than the first
the third rabbitt cost 80p less than the second
what is the cost of the first rabbitt

can someone please tell me the formula

2. Let the rabbits be $U_1, U_2\ and\ U_3$ respectively

You are told $U_1 + U_2 + U_3 = 19.70$

$U_2 = U_1 + 2$

$U_3 = U_2 - 0.8$

Can you use substitution to find U1? (My answer and working are in the spoiler if you wish to check but remember you're only cheating yourself if you don't bother trying)

Spoiler:
$U_3 = (U_1+2)-0.8 = U_1 + 1.2$ this make sense since £2-80p = £1.20

Back to our first equation

$U_1 + (U_1+2) + (U_1+1.2) = 19.70$

You can collect like terms and solve easily

Spoiler:
$3U_1 + 3.2 = 19.7$

$3U_1 = 16.50$

$U_1 = 5.50$

I get an answer of £5.50 which follows because we'd get

£5.50 + £7.50 + £6.70 = £13+£6.70 = £19.70

3. Once you're comfortable with the 3 variables method, you can do it quicker this way:
1st = a
2nd = a + 2
3rd = a + 2 - .8 = a + 1.2

(a) + (a+2) + (a+1.2) = 19.7
3a + 3.2 = 19.7
3a = 16.5
a = 5.5