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emilyphillips1681
02.03.2021 •
Mathematics
On a blueprint, the scale indicates that 4 cm represents 12 ft. What is the length of a room that is 5cm long and 3.5 cm wide on the blueprint?
The length of the room is
feet
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Ответ:
a. 3n₁ + 1.5n₂ = 18 and n₂ = 3n₁. b. there is no viable solution that meets Juan's conditions.
Step-by-step explanation:
a. Let n₁ be the number of roses and n₂ be the number of carnations. Now each rose costs $3. So the cost of n₁ roses will be 3n₁. Also, each carnation costs $1.5. So the cost of n₂ carnation will be 1.5n₂.
Since the total amount available is $18, then 3n₁ + 1.5n₂ = 18.
Also, he wants to buy 3 times as many carnations as roses. So, n₂ = 3n₁.
So, the system of equations are
3n₁ + 1.5n₂ = 18 and n₂ = 3n₁.
b. 3n₁ + 1.5n₂ = 18 and n₂ = 3n₁.
We solve the above system of equations by inserting the second equation into the first. So,
3n₁ + 1.5n₂ = 18
3n₁ + 1.5(3n₁.) = 18
3n₁ + 4.5n₁ = 18
7.5n₁ = 18
dividing both sides by 7.5, we have
n₁ = 18/7.5
= 2.4
So, n₂ = 3n₁
= 3(2.4)
= 7.2
Since n₁ = 2.4 and n₂ = 7.2 are not whole numbers, there is no viable solution that meets Juan's conditions.
Approximating n₁ = 2 and n₂ = 7. Inserting them into the first equation, we have
3n₁ + 1.5n₂ = 18
3(2) + 1.5(7) = 18
6 + 10.5 = 16.5 ≠ 18
Since L.H.S ≠ R.H.S, there is no viable solution that meets Juan's conditions.