Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10
each and short-sleeved shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeved shirts that can be purchased?
A minimum of ___ long-sleeved shirts can be purchased.
A maximum of ___ long-sleeved shirts can be purchased.
A minimum of ___ long-sleeved shirts can be purchased.
A maximum of ___ long-sleeved shirts can be purchased.
2 answers:
Answer:
The highest number of long-sleeved shirts that can be ordered is 8
and
The lowest number of long-sleeved shirts that can be acquired is 0
Step-by-step breakdown:
Let y denote the quantity of short sleeves and x indicate the quantity of long sleeves.
According to the stipulated conditions:
Members of a school club are purchasing coordinating shirts. They understand that a minimum of 25 members will opt for a shirt.
therefore, we have;
or
....[1]
Given that long-sleeved shirts are priced at $10 each and short-sleeved shirts at $5 each.
Thus;
The total expense for long sleeves amounts to 10x and
the total cost of short sleeves is 5yMoreover; the club has a budget that does not exceed $165
therefore;
......[2]
By plotting the inequality functions:
Graphing equations [1] and [2] produces a maximum at the coordinates (8, 17)
thus, x= 8.
Taking the minimum value of x =0 results in y falling between 25 and 33.
consequently, the solution space is situated between the intersecting lines to the left.
In conclusion, a maximum of 8 long-sleeved shirts can be obtained, while the minimum number of long-sleeved shirts that can be bought is 0
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The result of multiplying 10 by 6 hundreds equals 60 hundreds, which can also be expressed as 6 thousands.
Explanation
This can be simplified as follows:
- 10 times a given quantity of _____ hundreds results in 60 hundreds
- 60 hundreds convert to _____ thousands
We will divide this into two segments:
... Equation-1
... Equation-2
This straightforward multiplication relates to the place value system. We need to perform calculations to find the values of N and M.
Initially, let's focus on Equation-1.
We will move the variable M to one side of the equation in order to isolate it and solve for its value.
Both parts will be divided by 1,000, essentially being multiplied by .
Thus, we conclude with
Next, we process Equation-2 to derive M's value.
Rearranging this equation to place M on the left side appears as follows:
Again, both sides undergo division by 1,000, which translates to multiplication by .
This results in
- - - - - - -
Alternative approach for the second step:
60 hundreds equals to __ thousands
Additional resources
- A more detailed version of this topic
- 2 thousands 7 tens divided by 10 equals what?
- 100 is equivalent to 1/10 of which number?
Keywords: 10 times as many as, blank, hundreds, 60 hundreds, or, thousands, isolate, operations, multiply, divide, fraction, both sides, equal, the opposite, both sides are multiplied by, divided by, rearrange
