Question

The price of a certain type of cherry can range from \[\$ 2.50\] to \[\$ 3.00\] per pound and the price of a certain type of roll can range from \[\$ 0.80\] to \[\$ 1.10\] per dozen. To be sure of having enough money to buy c pounds of these cherries and r dozen of these rolls, a person needs at least how many dollars, in terms of c and r?
A.\[\dfrac{{{\text{c + r}}}}{{{\text{3 + 1}}{\text{.1}}}}\]
B.\[\dfrac{{\text{c}}}{{\text{3}}}{\text{ + }}\dfrac{{\text{r}}}{{{\text{1}}{\text{.1}}}}\]
C.\[{\text{2}}{\text{.5c + 0}}{\text{.8r}}\]
D.\[3c + 1.1r\]
E.\[\left( {3 + 1.1} \right)\left( {c + r} \right)\]

Answer 1

Hint: In this question we have given price of one pound cherry and one dozen rolls in certain range choose the lowest value of range as price after that multiply the price of one pound cherry with c(c is the number of pound of cherry which we want to buy) and multiply the price of one dozen roll with r(r is the number of dozen of roll which we want to buy) now add these two in order to get the answer.

Complete step-by-step answer:
We have given the price of a certain type of cherry can range from \[\$ 2.50\] to \[\$ 3.00\] per pound and the price of a certain type of roll can range from \[\$ 0.80\] to\[\$ 1.10\] per dozen.
But, if we have \[\$ 2.50\]then we can surely buy one pound of cherry and if we have \[\$ 0.80\]then we can surely buy one dozen rolls.
To buy one pound of cherry we have \[\$ 2.50\]
\[ \Rightarrow \] To buy c pound of cherry we required \[\$ 2.50 \times c\]\[ = \$ 2.50c\] \[ \ldots \left( 1 \right)\]
Similarly,
To buy one dozen of roll we have \[\$ 0.80\]
\[ \Rightarrow \]To buy r dozen of cherry we required\[\$ 0.80 \times r = \$ 0.80r\] \[ \ldots \left( 2 \right)\]
Now adding 1 and 2 we get,
\[\$ 2.50c + \$ 0.80r\]
Therefore, we can surely buy c pounds of cherries and a dozen rolls if we have\[\$ 2.50c + \$ 0.80r\].
Hence, option c. \[\$ 2.50c + \$ 0.80r\] is the correct answer.

Note: Steps to form a linear equation from a word problem is given below.
1.Read the given problem carefully and extract the values which are required to form an equation.
2.Denote the unknown by the variables as x, y,…
3.Translate the given word problem to the mathematical statements.
4.Form the linear equation using the conditions given in the problem.