Question

Shawna bought some strings of beads. The number of strings was 7 more than the number of beads on each string. There were 60 beads in all. How many beads were on each string?

Answer 1

Solution. Let x is the number of beads on each string, y is number of the strings. According to the condition of the problem, we have a system

$$\begin{cases} x-y=7 \\ x\times y=60 \end{cases}$$

From the first equation of the system

$$x=y+7$$

Substituting into the second equation of the system we obtain

$$x\times y=60 \implies (y+7)\times y=60$$

$$y^2+7y-60=0$$

The roots of the quadratic equation

$$y_1=5$$

$$y_2=-12<0$$

Therefore the number of beads on each string is equal to 5.

Answer. 5.