Problem of the Week

Updated at Feb 21, 2022 1:48 PM

This week we have another equation problem:

How can we solve the equation 55+44z=2526\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}?

Let's start!



55+44z=2526\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}

1
Cancel 44.
55+1z=2526\frac{5}{5+\frac{1}{z}}=\frac{25}{26}

2
Multiply both sides by 5+1z5+\frac{1}{z}.
5=2526(5+1z)5=\frac{25}{26}(5+\frac{1}{z})

3
Divide both sides by 2525.
525=126(5+1z)\frac{5}{25}=\frac{1}{26}(5+\frac{1}{z})

4
Simplify  525\frac{5}{25}  to  15\frac{1}{5}.
15=126(5+1z)\frac{1}{5}=\frac{1}{26}(5+\frac{1}{z})

5
Simplify  5+1z26\frac{5+\frac{1}{z}}{26}  to  526+1z26\frac{5}{26}+\frac{\frac{1}{z}}{26}.
15=526+1z26\frac{1}{5}=\frac{5}{26}+\frac{\frac{1}{z}}{26}

6
Simplify  1z26\frac{\frac{1}{z}}{26}  to  126z\frac{1}{26z}.
15=526+126z\frac{1}{5}=\frac{5}{26}+\frac{1}{26z}

7
Subtract 526\frac{5}{26} from both sides.
15−526=126z\frac{1}{5}-\frac{5}{26}=\frac{1}{26z}

8
Simplify  15−526\frac{1}{5}-\frac{5}{26}  to  1130\frac{1}{130}.
1130=126z\frac{1}{130}=\frac{1}{26z}

9
Multiply both sides by 26z26z.
1130×26z=1\frac{1}{130}\times 26z=1

10
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
1×26z130=1\frac{1\times 26z}{130}=1

11
Simplify  1×26z1\times 26z  to  26z26z.
26z130=1\frac{26z}{130}=1

12
Simplify  26z130\frac{26z}{130}  to  z5\frac{z}{5}.
z5=1\frac{z}{5}=1

13
Multiply both sides by 55.
z=1×5z=1\times 5

14
Simplify  1×51\times 5  to  55.
z=5z=5

Done
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