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    Create an algebraic expression from a word problem, simplify, and evaluate in dollars version

    \( \begingroup \)

    Question 1

    Jerry eats a lot of sweets. You are trying to work out the cost of the sweets that Jerry ate last week.

    Jerry ate $\var{a1}$ packets of lollipops, $\var{b1}$ packets of toffee and $\simplify{{c1}}$ packets of jelly sweets.

    You know that a packet of toffee costs $1 more than a packet of lollipops, and a packet of jelly sweets costs half as much as a packet of toffees.

    a)

    Let the cost of a packet of lollipops be $x.

    Write an expression in terms of $x$ for the cost of each kind of sweet:

    Lollipops: $interpreted as

    Toffees: $interpreted as

    Jelly sweets: $interpreted as

    Score: 0/3

    Feedback for a).

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      Or, you could:

        There's nothing more to do from here.

        b)

        Write an algebraic expression for the overall cost of the sweets Jerry ate, in terms of $x$.

        $interpreted as

        Score: 0/1

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          Or, you could:

            There's nothing more to do from here.

            c)

            Now simplify your expression for the total cost.

            $interpreted as

            Score: 0/1

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              Or, you could:

                There's nothing more to do from here.

                d)

                You find out that a packet of lollipops costs $2.

                Calculate Jerry's total expenditure on sweets last week.

                $interpreted as

                Score: 0/1

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                  Or, you could:

                    There's nothing more to do from here.

                    Advice

                    a)

                    We are told that the price of a packet of lollipops is represented by the letter $x$.

                    A packet of toffee costs $£1$ more than a packet of lollipops, i.e. $x+1$.

                    A packet of jelly sweets costs half as much as a packet of toffee, so $\frac{1}{2}(x+1)$.

                    b)

                    To find the total cost, multiply the expressions above for the cost of each kind of sweet by the number of packets eaten, and add them together.

                    Without simplifying, we obtain:

                    \begin{align}
                    \text{Cost} &= \simplify[]{{a1}x+{b1}(x+1) + {c1}*(1/2)*(x+1)} \\
                    &= \simplify[]{{a1}x+{b1}(x+1) + {c1/2}*(x+1)}
                    \text{.}
                    \end{align}

                    c)

                    The first step in simplifying this expression is to expand both sets of brackets:

                    \begin{align}
                    \simplify[]{ {a1}x + {b1}(x+1) + {c1/2}*(x+1)} &= \simplify[]{ {a1}x + {b1}x + {b1}*1 + {c1/2}x + {c1/2}*1} \\
                    &= \simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } \text{.}
                    \end{align}

                    Finally, collect like terms:

                    \begin{align}
                    \simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } &= \simplify[]{ {a1+b1+c1/2}x + {b1+c1/2} } \text{.}
                    \end{align}

                    d)

                    Once we know that the price of a packet of lollipops is $£2$, we can substitute this for $x$ in the equation above.

                    \begin{align}
                    \text{Cost}&=\simplify{ {a1+b1+c1/2}x+{b1+c1/2} }\\
                    &=\var{a1+b1+c1/2} \times 2+\var{b1+c1/2} \\
                    &=\var{(a1+b1+c1/2)*2+b1+c1/2} \text{.}
                    \end{align}

                    So Jerry spent $£\var{total}$ on sweets last week.
                    \( \endgroup \)

                    Score: 0/6

                    Total 0/6
                    Created using Numbas, developed by Newcastle University.