Maths-
General
Easy

Question

Lucy plans to spend between $50 and $ 65, inclusive on packages of charms. If she buy 5 packages of beads at $4.95 each, how many packages of charms at $6.55 can lucy buy while staying within her budget?

hintHint:

If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
 

The correct answer is: Hence, Lucy can buy 4 to 6 charms staying within her budget.


    Lucy bought 5 packages of beads
    Cost of 5 packages of beads = $4.95  5 = $24.75
    Let’s say that number of packages of charms bought by Lucy is n
    Cost of n packets of charms = $6.55n
    Total money spent by Lucy = $(6.55n + 24.75)
    It is given that Lucy can spend between $50 and $ 65
    So, $50 ≤ $(6.55n + 24.75) ≤ $65
    Solving the inequality
    50 ≤ 6.55n + 24.75 ≤ 65
    Subtracting 24.75 on all sides
    25.25 ≤ 6.55n ≤ 40.25
    Dividing 6.55 on all sides
    3.85 ≤ n ≤ 6.14 or 4 ≤ n ≤ 6
    Final Answer:
    Hence, Lucy can buy 4 to 6 charms staying within her budget.

    When two simple inequalities are combined, the result is a compound inequality. For example, a sentence with two inequality statements connected by the words "or" or "and" is a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. So it is when the solution sets for the various statements cross over or intersect. E.g., for "AND": Solve the statement where x: 3 x + 2 < 14 and 2 x – 5 > –11. The solution set is
    { x| x > –3 and x < 4}. All the numbers present to the left of 4 are denoted by x < 4, and the numbers to the right of -3 are represented by x > -3. The intersection of these two graphs is comprised of all integers between -3 and 4.

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