Question 629384
The 1st thing to do is define the unknowns
Let {{{ a }}} = the larger of the 2 numbers
Let {{{ b }}} = the smaller of the 2 numbers
given:
(1) {{{ a = 3b + 3 }}}
( The larger of two numbers is 3 more than 3 times the smaller. )
(2) {{{ a - b = 15 }}}
( If the smaller number is subtracted from the larger, the result is 15. )
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There are 2 equations and 2 unknowns, so
the problem is solvable.
Substitute (1) into (2)
(2) {{{ 3b + 3 - b = 15 }}}
(2) {{{ 2b + 3 = 15 }}}
(2) {{{ 2b = 12 }}}
(2) {{{ b = 6 }}}
and, since
(1) {{{ a = 3b + 3 }}}
(1) {{{ a = 3*6 + 3 }}}
(1) {{{ a = 18 + 3 }}}
(1) {{{ a = 21 }}}
The numbers are 21 and 6
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check:
(1) {{{ a = 3b + 3 }}}
(1) {{{ 21 = 3*6 + 3 }}}
(1) {{{ 21 = 18 + 3 }}}
(1) {{{ 21 = 21 }}}
and
(2) {{{ a - b = 15 }}}
(2) {{{ 21 - 6 = 15 }}}
(2) {{{ 21 = 15 + 6 }}}
(20 {{{ 21 = 21 }}}
OK