Answer:
{a}p + 0.2m = 6
0.8m = 4
or 5p + m = 30
m = 5
{b} 5 lb peanuts and 5 lb mixture
Step-by-step explanation:
m1 → desired mixture with composition : 60% peanuts and 40% almonds and weight : 10 lb
⇒weight of peanuts in m1 = 60% × 5 = 6 lb
and weight of almonds in m1 is 4 lb
m2 → mixture with composition : 20% peanuts and 80% almonds and weight : m pounds
⇒weight of peanuts in m2 = 0.2m
and weight of almonds in m2 = 0.8m
p → weight (in pounds) of peanuts added to m2 to make m1
{a}
add p pounds of peanuts to m2 to make m1
equating weights of peanuts and almonds:
p + 0.2m = 6
0.8m = 4
{b}
equation gives m = [tex]\frac{4}{0.8}[/tex] ⇒ m = 5 lb
Using this in the [tex]1^{st}[/tex] equation:
p + 1 = 6 ⇒ p = 5 lb
Answer:
a) p + m = 10 and [tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex]
b) The mixing amount is 5 lb peanut and 5 lb mixture.
Step-by-step explanation:
Given that p pounds of peanuts and m pounds of the 80% almond and 20% peanut mixture are used to make 10 pounds of 60% peanuts and 40% of almonds mixture.
Now, we can write that p + m = 10 ........ (1)
Now, m pounds of 80% almond and 20% peanut mixture contain 0.2m pounds of peanuts and 0.8m pounds of almonds.
Now, from the condition given it can be written that
[tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex] .......... (2)
⇒ [tex]\frac{p + 0.2m}{0.8m} = \frac{3}{2}[/tex]
⇒ 2p + 0.4m = 2.4m
⇒ 2p = 2m
⇒ p = m
Now from equation (1) we get p = m = 5 pounds.
a) Therefore, equations (1) and (2) are the system of equations that models the situation.
b) The mixing amount is 5 lb peanut and 5 lb mixture. (Answer)
