Help with math problem solving problem!?

A) assume x is the number of words

so

the cost of the union Telegraph = 1 +0.03x

the cost of the Corrugated Telegraph = 0.4 + 0.05x

as the cost is the same, then:

1 + 0.03x = 0.4 +0.05x

0.6 = 0.02x

x = 0.6/0.02 = 30 words

B) if he uses 30 words then it wouldn't matter, but if he used less or more then:

for x< 30

take x =29

the cost of the union Telegraph = 1 +0.03x

= 1 + 0.03(29) = 1.87

the cost of the Corrugated Telegraph = 0.4 + 0.05x

= 0.4 +0.05(29)

= 1.85

so he should use the Corrugated Telegraph if it is less than 30

now take x>30, lets say 31

the cost of the union Telegraph = 1 +0.03x

= 1 + 0.03(31) = 1.93

the cost of the Corrugated Telegraph = 0.4 + 0.05x

= 0.4 +0.05(29)

= 1.95

so he should use the union Telegraph if it is more than 30 words

so the answe will be:

x <= 30, use the Corrugated Telegraph

x >= 30, use the union Telegraph

unionTelegraph's cost = $1 + $0.03 * (words)

corrugatedTelegraph's cost = $0.40 + $0.05 * (words)

He discovers that both costs are the same: unionTelegraph's cost = corrugatedTelegraph's cost

$1 + $0.03 * (w) = $0.40 + $0.05 * (w)

1 + 0.03w = 0.40 + 0.05w .......... I just rewrote it without dollar sign and using 'w' for #words

0.6 + 0.03w = 0.05w

0.6 = 0.02w

30 = w = words

A) There were 30 words in Shorty's telegram.

B) For part B, it should be understood

....that one telegraph will be cheaper when you have few words,

....the other telegraph will be cheaper when you have a lot of words,

....and both telegraphs cost the same for a certain amount of words.

We already know that at 30 words, both telegraphs would cost the same.

So what if you had less than 30 words? Say... 10 words? Well, I don't know, let's find out!

Plug in, words = 10 into the equations:

unionTelegraph's cost = $1 + $0.03 * (10) = $1.30

corrugatedTelegraph's cost = $0.40 + $0.05 * (10) = $0.90

corrugatedTelegraph's cost is cheaper for words < 30

We can then reason that unionTelegraph's cost is cheaper for words > 30

Edit: /* By the way, note that if words = 30, there is no "better" company or "better" rate. */

If you want to make sure, which you should, just choose any number larger than 30 and plug it into the equations to make sure unionTelegraph's cost would be cheaper.

Hope I've helped.

At Union, the cost can be calculated using the formula C = .03w + 1

At Corrugated the cost can be calculated using the formula C = .05w + .4

Since they both cost the same for Shorty's message, then we can create an equation and solve for w (words).

.03w + 1 = .05w + .4

.02w = .6

w = 30

Shorty's message had 30 words which is the break-even point. If your message has less than 30 words, it would cost less to use Corrugated Telegraph because the fixed cost (40 cents) is lower. If your message has more than 30 words, it would cost less to use Union because their cost per word is lower.

No. of words—w:

$1.00 + 0.03w = $0.40 + 0.05w

$0.02w = $0.60

w = 30

Answer: 30 words

If more than 30 words Telegraph Co. is better; if less than 30 words Corrugated Telegraph Co. is more advantageous; else, they'll cost the same.

Let x = number of girls, and y = number of boys. Therefore we get 3x + 4y = 92 and x + y = 26 so 4y = 92 - 3x and y = 26 - x so 4y = 92 - 3x and 4y = 104 - 4x (multiply by 4) which implies 92 - 3x = 104 - 4x so -3x = 12 - 4x so x =12 and y = 26 - 12 = 14 ie there are 12 girls and 14 boys in the class.

You need to decide whether to purchase a $10,000 copier or lease it for $320 per month for three years for the office. The past year your office made 50,000 copies, purchased $500 in toner supplies and had $800 in repair and maintenance expense. You do not anticipate a significant increase in use of the copier for the next three years. The lease agreement provides for toner, repair and maintenance. Assume you will supply the necessary paper for all copying jobs regardless of option chosen. Which option will save your company the most money?

What is the cost in the first year for purchasing the copier if you choose the purchase option?