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jekas [21]
3 years ago
14

Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two num

bers.
The sum of two numbers is 75. One number is 23 more than the other. Find the numbers.
Mathematics
1 answer:
eduard3 years ago
8 0

Answer:

The value of two numbers is x=49 and y=26 and the corresponding equation for the given condition is x +y =75  

<u>Explanation:</u>

Given:

Sum of two numbers is 75

One number is 23 more than other

To find:

Frame the equation for the above condition and find the value of two numbers.

Solution:

From the given we know that the sum of two numbers is 75  

Let x and y be the numbers, such that the equation is framed as

x +y =75

And we also know that one number is 23 more than other, so we can say either x or y has a greater one

Here I say x is 23 more than y such that,

x=23+y

Substitute the value of x in the equation and we know

x + y=75 and x=23+y we get,

23+y+y=75

23+2y=75

2y=75-23

2y=52

y=26

Since x=23+y as already stated we get as

x=23+26=49

Result:

Thus the equation for the above given conditions is x +y =75 and the values of two number is 49 and 26

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40% of the memberships sold by Gym A were gold memberships.
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Answer:

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

Step-by-step explanation:

Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.  

Which statement must be true?

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.

c) Gym A sold more gold membership than Gym A did.

d) If Gym B sold 50 membership, 25 would be gold memberships.

Given: Gym A have sold 40% gold membership of total membership.

Gym B have sold 25% gold membership of total membership.

Lets take option A first to find if it is true statement.

As per option A, There are total number of membership is 80.

∵ Gym A has sold 40% gold membership.

∴ Gym A gold membership= 40\% \times 80

⇒ Gym A gold membership= \frac{40}{100} \times 80= 32 member.

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Now, Gym B

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Next finding difference gold membership for Gym A and Gym B

32-20= 12 \ membership

Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.

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