A manufacturer produces three types of radios: deluxe, standard and economy. Each radio uses three different types of transistors: P, Q and R. The deluxe radio uses 2 P's, 7 Q's and 1 R. The standard contains 2 P's, 3 Q's and 1 R, and the economy model requires 1 P, 2 Q's and 2 R's.

Question

A manufacturer produces three types of radios: deluxe, standard and economy. Each radio uses three different types of transistors: P, Q and R. The deluxe radio uses 2 P's, 7 Q's and 1 R. The standard contains 2 P's, 3 Q's and 1 R, and the economy model requires 1 P, 2 Q's and 2 R's.

Answer 1

See:

http://www.jiskha.com/display.cgi?id=1310358660

Answer 2

To answer this question, we can use a system of equations. Let's assign variables to represent the number of each type of transistor used in each type of radio.

Let:
- D represent the number of deluxe radios produced
- S represent the number of standard radios produced
- E represent the number of economy radios produced

Now, we can write the following equations based on the information given:

Equation 1: 2P + 7Q + 1R = deluxe radios
Equation 2: 2P + 3Q + 1R = standard radios
Equation 3: 1P + 2Q + 2R = economy radios

These equations represent the number of each type of transistor used in each type of radio produced.

To solve these equations, we could either use substitution or elimination method.

Using the elimination method, we can subtract Equation 2 from Equation 1 to eliminate the 'P' term:
(2P + 7Q + 1R) - (2P + 3Q + 1R) = deluxe radios - standard radios
Simplifying, we get: 4Q = deluxe radios - standard radios ...(1)

Next, we subtract Equation 3 from Equation 2 to eliminate the 'P' term:
(2P + 3Q + 1R) - (1P + 2Q + 2R) = standard radios - economy radios
Simplifying, we get: Q - R = standard radios - economy radios ...(2)

Now, we have two equations (equations 1 and 2) that we can use to solve for the variables 'Q' and 'R'.

Using Equation (1), we can substitute its expression for 'deluxe radios - standard radios' into Equation (2):
Q - R = 4Q ...(2)

Simplifying, we get: R = 3Q ...(3)

Now we can use Equation (3) to substitute 'R' in Equation (2):
Q - (3Q) = standard radios - economy radios
Simplifying, we get: -2Q = standard radios - economy radios
This equation helps us understand the relationship between the 'Q' values for standard radios and economy radios.

At this point, we have a system of equations including Equation (3) (-2Q = standard radios - economy radios) and Equation (1) (4Q = deluxe radios - standard radios).

Using these two equations, we can substitute the value we obtained for 'deluxe radios - standard radios' from Equation (1) into Equation (3):
R = 3Q
Substituting the value of 'deluxe radios - standard radios' which is equal to 4Q, we get:
R = 3Q = 4Q

Simplifying, we get: Q = 0

Substituting the value of 'Q' back into Equation (3), we get:
R = 3(0) = 0

Now that we have values for 'Q' and 'R', we can substitute them into one of the original equations to solve for 'P'.

Let's use Equation (2):
2P + 3Q + 1R = standard radios
Substituting Q = 0 and R = 0, we get:
2P + 0 + 0 = standard radios
Simplifying, we get: 2P = standard radios
Dividing both sides by 2, we get: P = standard radios/2

Therefore, for this specific scenario as determined by the given equations, the number of transistors for each type of radio would be:

- Deluxe radio: 2 P's, 0 Q's, and 0 R's
- Standard radio: standard radios/2 P's, 0 Q's, and 0 R's
- Economy radio: 1 P, 2 Q's, and 2 R's

The exact number of radios produced, represented by the variables D (deluxe), S (standard), and E (economy), would depend on the context or additional information given.