Question

Could someone help me please quickly

Answer 1

$6 for each pound of almonds

Answer 2

Each Almond costs $1.5

Each Jelly bean costs $3.75

Explanation:

Let Almonds be a

Let Jelly beans be j

- For the first case;

3$ of Almond + 2$ of Jelly beans = $12

`{ \tt{3a + 2j = 12 - - - eqn(i)}}`

- For the second case;

5$ of Almond + 6$ of Jelly beans = $30

`{ \tt{5a + 6j = 30 - - - eqn(ii)}}`

✍️ From equation (i), make 2j the subject;

`{ \tt{2j = 12 - 3a - - - eqn(iii)}}`

✍️ Substitute 6j in eqn (ii) with 2j in eqn (iii)

`{ \tt{5a + 6j = 30}} \: \: \: \: \: \: \\ \\ { \tt{5a + 3(2j) = 30}} \\ \\ { \tt{5a + 3(12 - 3a) = 30}} \\ \\ { \tt{5a + 36 - 9a = 30}} \\ \\ { \tt{ - 4a + 36 = 30}} \\ \\ { \tt{ - 4a = - 6 }} \\ \\ { \tt{a = 1.5}} \\ \\ { \colorbox{silver}{almond = 1.5 \: pounds}}`

From eqn(iii)

`{ \tt{2j = 12 - 3a}} \\ \\ { \tt{2j = 12 - 3(1.5)}} \\ \\ { \tt{2j = 7.5}} \\ \\ { \tt{j = 3.75}} \\ \\ { \colorbox{silver}{jelly \: beans = 3.75}}`