Word Problems Calculator

x,y — Number

x+y=S, x−y=D → x=(S+D)/2

A+k — Age

In k years: A₀+k and B₀+k

d=rt — Distance

d=rt; meet: (r₁+r₂)t=d

c₁q₁ — Mixture

c₁q₁+c₂q₂=c_T(q₁+q₂)

1/t — Work

1/t₁+1/t₂=1/t_together

Prt — Interest

I=Prt; A=P(1+r)ᵗ

□△○ — Geometry

P=2(L+W); A=½bh; A=πr²

¢$ — Coins

Σ(value×count) = total value

Sum+Diff $x=\frac{S+D}{2},\;y=\frac{S-D}{2}$

Age (twice) $A_0+k=2(B_0+k)\Rightarrow k=A_0-2B_0$

Distance $d=r\cdot t$

Meeting $(r_1+r_2)\cdot t=d_{\text{total}}$

Catch-Up $r_2 t=r_1(t+h)$

Round Trip $r_{\text{avg}}=\frac{2r_1r_2}{r_1+r_2}$

Mixture $c_1q_1+c_2q_2=c_T(q_1+q_2)$

Work $\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{t_T}$

Simple Int. $I=P\cdot r\cdot t$

Compound $A=P(1+r)^t$

Rule of 72 $t_{\text{double}}\approx 72/r$

Rect Area $A=L\cdot W$

Rect Perim $P=2(L+W)$

Triangle $A=\tfrac{1}{2}bh$

Heron's $A=\sqrt{s(s-a)(s-b)(s-c)}$

Circle $A=\pi r^2,\;C=2\pi r$

Incl-Excl $L+W=P/2,\;LW=A\Rightarrow t^2-\frac{P}{2}t+A=0$

Coin $v_1 n_1+v_2 n_2=V,\;n_1+n_2=N$

Ax=BWord Problems Calculator