Question Write a system of equations to find the cost of pens and pencils, where $x$ is the number of pens and $y$ is the number of pencils. Gabby bought $4$ pens and $5$ pencils for $\$ 6.71$ , and Sydney bought $5$ pens and $3$ pencils for $\$ 7.12$ .

Studdy Solution

STEP 1

Assumptions1. Gabby bought4 pens and5 pencils for $6.71. Sydney bought5 pens and3 pencils for$ 7.123. Let $x$ represent the cost of one pen4. Let $y$ represent the cost of one pencil

STEP 2

We can write the first equation based on the information about Gabby's purchase. The total cost of Gabby's purchase is the cost of the pens plus the cost of the pencils.
$4x +5y =6.71$

STEP 3

Similarly, we can write the second equation based on the information about Sydney's purchase. The total cost of Sydney's purchase is the cost of the pens plus the cost of the pencils.
$5x +3y =7.12$ So, the system of equations based on the given information is\begin{cases} x +5y =6.71\\5x +3y =7.12\end{cases}

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